id	sid	tid	token	lemma	pos
ejpam-412	1	1	8_xxx_erturk.dvi	8_xxx_erturk.dvi	PROPN
ejpam-412	1	2	european	european	ADJ
ejpam-412	1	3	journal	journal	PROPN
ejpam-412	1	4	of	of	ADP
ejpam-412	1	5	pure	pure	ADJ
ejpam-412	1	6	and	and	CCONJ
ejpam-412	1	7	applied	apply	VERB
ejpam-412	1	8	mathematics	mathematic	NOUN
ejpam-412	1	9	vol	vol	NOUN
ejpam-412	1	10	.	.	PROPN
ejpam-412	2	1	2	2	NUM
ejpam-412	2	2	,	,	PUNCT
ejpam-412	2	3	no	no	INTJ
ejpam-412	2	4	.	.	NOUN
ejpam-412	2	5	3	3	NUM
ejpam-412	2	6	,	,	PUNCT
ejpam-412	2	7	2009	2009	NUM
ejpam-412	2	8	,	,	PUNCT
ejpam-412	2	9	(	(	PUNCT
ejpam-412	2	10	426	426	NUM
ejpam-412	2	11	-	-	NUM
ejpam-412	2	12	447	447	NUM
ejpam-412	2	13	)	)	PUNCT
ejpam-412	2	14	issn	issn	PROPN
ejpam-412	2	15	1307	1307	NUM
ejpam-412	2	16	-	-	SYM
ejpam-412	2	17	5543	5543	NUM
ejpam-412	2	18	–	–	PUNCT
ejpam-412	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-412	2	20	solutions	solution	NOUN
ejpam-412	2	21	of	of	ADP
ejpam-412	2	22	different	different	ADJ
ejpam-412	2	23	types	type	NOUN
ejpam-412	2	24	of	of	ADP
ejpam-412	2	25	the	the	DET
ejpam-412	2	26	linear	linear	ADJ
ejpam-412	2	27	and	and	CCONJ
ejpam-412	2	28	nonlinear	nonlinear	ADJ
ejpam-412	2	29	higher	high	ADJ
ejpam-412	2	30	-	-	PUNCT
ejpam-412	2	31	order	order	NOUN
ejpam-412	2	32	boundary	boundary	ADJ
ejpam-412	2	33	value	value	NOUN
ejpam-412	2	34	problems	problem	NOUN
ejpam-412	2	35	by	by	ADP
ejpam-412	2	36	differential	differential	ADJ
ejpam-412	2	37	transformation	transformation	NOUN
ejpam-412	2	38	method	method	PROPN
ejpam-412	2	39	i.	i.	PROPN
ejpam-412	2	40	h.	h.	PROPN
ejpam-412	2	41	abdel	abdel	PROPN
ejpam-412	2	42	-	-	PUNCT
ejpam-412	2	43	halim	halim	PROPN
ejpam-412	2	44	hassan1	hassan1	PROPN
ejpam-412	2	45	,	,	PUNCT
ejpam-412	2	46	vedat	vedat	NOUN
ejpam-412	2	47	suat	suat	NOUN
ejpam-412	2	48	ertürk2∗	ertürk2∗	PROPN
ejpam-412	2	49	1	1	NUM
ejpam-412	2	50	department	department	NOUN
ejpam-412	2	51	of	of	ADP
ejpam-412	2	52	mathematics	mathematic	NOUN
ejpam-412	2	53	,	,	PUNCT
ejpam-412	2	54	faculty	faculty	NOUN
ejpam-412	2	55	of	of	ADP
ejpam-412	2	56	science	science	NOUN
ejpam-412	2	57	,	,	PUNCT
ejpam-412	2	58	zagazig	zagazig	PROPN
ejpam-412	2	59	university	university	PROPN
ejpam-412	2	60	,	,	PUNCT
ejpam-412	2	61	zagazig	zagazig	PROPN
ejpam-412	2	62	,	,	PUNCT
ejpam-412	2	63	egypt	egypt	PROPN
ejpam-412	2	64	2	2	NUM
ejpam-412	2	65	department	department	NOUN
ejpam-412	2	66	of	of	ADP
ejpam-412	2	67	mathematics	mathematic	NOUN
ejpam-412	2	68	,	,	PUNCT
ejpam-412	2	69	faculty	faculty	NOUN
ejpam-412	2	70	of	of	ADP
ejpam-412	2	71	arts	art	NOUN
ejpam-412	2	72	and	and	CCONJ
ejpam-412	2	73	sciences	science	NOUN
ejpam-412	2	74	,	,	PUNCT
ejpam-412	2	75	ondokuz	ondokuz	PROPN
ejpam-412	2	76	mayıs	mayıs	PROPN
ejpam-412	2	77	university	university	PROPN
ejpam-412	2	78	,	,	PUNCT
ejpam-412	2	79	55139	55139	NUM
ejpam-412	2	80	,	,	PUNCT
ejpam-412	2	81	samsun	samsun	NOUN
ejpam-412	2	82	,	,	PUNCT
ejpam-412	2	83	turkey	turkey	PROPN
ejpam-412	2	84	abstract	abstract	NOUN
ejpam-412	2	85	.	.	PUNCT
ejpam-412	3	1	in	in	ADP
ejpam-412	3	2	[	[	X
ejpam-412	3	3	12	12	NUM
ejpam-412	3	4	]	]	X
ejpam-412	3	5	,	,	PUNCT
ejpam-412	3	6	a	a	DET
ejpam-412	3	7	numerical	numerical	ADJ
ejpam-412	3	8	comparison	comparison	NOUN
ejpam-412	3	9	between	between	ADP
ejpam-412	3	10	the	the	DET
ejpam-412	3	11	differential	differential	ADJ
ejpam-412	3	12	transform	transform	NOUN
ejpam-412	3	13	method	method	NOUN
ejpam-412	3	14	and	and	CCONJ
ejpam-412	3	15	adomian	adomian	NOUN
ejpam-412	3	16	decomposition	decomposition	NOUN
ejpam-412	3	17	method	method	NOUN
ejpam-412	3	18	for	for	ADP
ejpam-412	3	19	solving	solve	VERB
ejpam-412	3	20	fourth	fourth	ADJ
ejpam-412	3	21	-	-	PUNCT
ejpam-412	3	22	order	order	NOUN
ejpam-412	3	23	boundary	boundary	ADJ
ejpam-412	3	24	value	value	NOUN
ejpam-412	3	25	problems	problem	NOUN
ejpam-412	3	26	was	be	AUX
ejpam-412	3	27	presented	present	VERB
ejpam-412	3	28	.	.	PUNCT
ejpam-412	4	1	in	in	ADP
ejpam-412	4	2	this	this	DET
ejpam-412	4	3	article	article	NOUN
ejpam-412	4	4	,	,	PUNCT
ejpam-412	4	5	we	we	PRON
ejpam-412	4	6	use	use	VERB
ejpam-412	4	7	the	the	DET
ejpam-412	4	8	differential	differential	ADJ
ejpam-412	4	9	transformation	transformation	NOUN
ejpam-412	4	10	method	method	NOUN
ejpam-412	4	11	(	(	PUNCT
ejpam-412	4	12	dtm	dtm	PROPN
ejpam-412	4	13	)	)	PUNCT
ejpam-412	4	14	to	to	PART
ejpam-412	4	15	solve	solve	VERB
ejpam-412	4	16	the	the	DET
ejpam-412	4	17	linear	linear	ADJ
ejpam-412	4	18	and	and	CCONJ
ejpam-412	4	19	non	non	ADJ
ejpam-412	4	20	-	-	ADJ
ejpam-412	4	21	linear	linear	ADJ
ejpam-412	4	22	higher	high	ADJ
ejpam-412	4	23	-	-	PUNCT
ejpam-412	4	24	order	order	NOUN
ejpam-412	4	25	boundary	boundary	ADJ
ejpam-412	4	26	value	value	NOUN
ejpam-412	4	27	problems	problem	NOUN
ejpam-412	4	28	(	(	PUNCT
ejpam-412	4	29	hobvps	hobvps	PROPN
ejpam-412	4	30	)	)	PUNCT
ejpam-412	4	31	.	.	PUNCT
ejpam-412	5	1	the	the	DET
ejpam-412	5	2	method	method	NOUN
ejpam-412	5	3	proved	prove	VERB
ejpam-412	5	4	to	to	PART
ejpam-412	5	5	be	be	AUX
ejpam-412	5	6	very	very	ADV
ejpam-412	5	7	successful	successful	ADJ
ejpam-412	5	8	and	and	CCONJ
ejpam-412	5	9	powerful	powerful	ADJ
ejpam-412	5	10	in	in	ADP
ejpam-412	5	11	computing	compute	VERB
ejpam-412	5	12	such	such	ADJ
ejpam-412	5	13	elements	element	NOUN
ejpam-412	5	14	.	.	PUNCT
ejpam-412	6	1	the	the	DET
ejpam-412	6	2	specific	specific	ADJ
ejpam-412	6	3	problems	problem	NOUN
ejpam-412	6	4	chosen	choose	VERB
ejpam-412	6	5	for	for	ADP
ejpam-412	6	6	this	this	DET
ejpam-412	6	7	purpose	purpose	NOUN
ejpam-412	6	8	is	be	AUX
ejpam-412	6	9	that	that	PRON
ejpam-412	6	10	of	of	ADP
ejpam-412	6	11	the	the	DET
ejpam-412	6	12	different	different	ADJ
ejpam-412	6	13	types	type	NOUN
ejpam-412	6	14	of	of	ADP
ejpam-412	6	15	higher	high	ADJ
ejpam-412	6	16	order	order	NOUN
ejpam-412	6	17	(	(	PUNCT
ejpam-412	6	18	e.g.	e.g.	ADV
ejpam-412	6	19	fifth	fifth	ADJ
ejpam-412	6	20	,	,	PUNCT
ejpam-412	6	21	sixth	sixth	ADJ
ejpam-412	6	22	,	,	PUNCT
ejpam-412	6	23	ninth	ninth	ADJ
ejpam-412	6	24	,	,	PUNCT
ejpam-412	6	25	tenth	tenth	ADJ
ejpam-412	6	26	and	and	CCONJ
ejpam-412	6	27	twelfth	twelfth	ADJ
ejpam-412	6	28	)	)	PUNCT
ejpam-412	6	29	boundary	boundary	ADJ
ejpam-412	6	30	value	value	NOUN
ejpam-412	6	31	problems	problem	NOUN
ejpam-412	6	32	.	.	PUNCT
ejpam-412	7	1	the	the	DET
ejpam-412	7	2	differential	differential	ADJ
ejpam-412	7	3	transformation	transformation	NOUN
ejpam-412	7	4	(	(	PUNCT
ejpam-412	7	5	dt	dt	NOUN
ejpam-412	7	6	)	)	PUNCT
ejpam-412	7	7	solutions	solution	NOUN
ejpam-412	7	8	are	be	AUX
ejpam-412	7	9	compared	compare	VERB
ejpam-412	7	10	with	with	ADP
ejpam-412	7	11	the	the	DET
ejpam-412	7	12	theoretical	theoretical	ADJ
ejpam-412	7	13	solution	solution	NOUN
ejpam-412	7	14	.	.	PUNCT
ejpam-412	8	1	it	it	PRON
ejpam-412	8	2	is	be	AUX
ejpam-412	8	3	shown	show	VERB
ejpam-412	8	4	that	that	SCONJ
ejpam-412	8	5	the	the	DET
ejpam-412	8	6	solutions	solution	NOUN
ejpam-412	8	7	obtained	obtain	VERB
ejpam-412	8	8	from	from	ADP
ejpam-412	8	9	the	the	DET
ejpam-412	8	10	technique	technique	NOUN
ejpam-412	8	11	have	have	VERB
ejpam-412	8	12	a	a	DET
ejpam-412	8	13	very	very	ADV
ejpam-412	8	14	high	high	ADJ
ejpam-412	8	15	degree	degree	NOUN
ejpam-412	8	16	of	of	ADP
ejpam-412	8	17	accuracy	accuracy	NOUN
ejpam-412	8	18	.	.	PUNCT
ejpam-412	9	1	2000	2000	NUM
ejpam-412	9	2	mathematics	mathematic	NOUN
ejpam-412	9	3	subject	subject	NOUN
ejpam-412	9	4	classifications	classification	NOUN
ejpam-412	9	5	:	:	PUNCT
ejpam-412	9	6	35c10	35c10	NUM
ejpam-412	9	7	,	,	PUNCT
ejpam-412	9	8	74s30	74s30	NUM
ejpam-412	9	9	,	,	PUNCT
ejpam-412	9	10	65l10	65l10	NUM
ejpam-412	9	11	,	,	PUNCT
ejpam-412	9	12	34b05	34b05	NUM
ejpam-412	9	13	,	,	PUNCT
ejpam-412	9	14	34b15	34b15	NUM
ejpam-412	9	15	.	.	PUNCT
ejpam-412	10	1	∗corresponding	∗corresponde	VERB
ejpam-412	10	2	author	author	NOUN
ejpam-412	10	3	.	.	PUNCT
ejpam-412	11	1	email	email	NOUN
ejpam-412	11	2	addresses	address	NOUN
ejpam-412	11	3	:	:	PUNCT
ejpam-412	11	4	ismhalim	ismhalim	PROPN
ejpam-412	11	5	�	�	PROPN
ejpam-412	11	6	hotmail	hotmail	NOUN
ejpam-412	11	7	.	.	PUNCT
ejpam-412	12	1	om	om	PROPN
ejpam-412	12	2	(	(	PUNCT
ejpam-412	12	3	i.	i.	PROPN
ejpam-412	12	4	abdel	abdel	PROPN
ejpam-412	12	5	-	-	PUNCT
ejpam-412	12	6	halim	halim	PROPN
ejpam-412	12	7	)	)	PUNCT
ejpam-412	12	8	,	,	PUNCT
ejpam-412	12	9	vserturk�omu.edu.tr	vserturk�omu.edu.tr	ADV
ejpam-412	12	10	(	(	PUNCT
ejpam-412	12	11	v.	v.	ADP
ejpam-412	12	12	ertürk	ertürk	NOUN
ejpam-412	12	13	)	)	PUNCT
ejpam-412	12	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-412	13	1	426	426	NUM
ejpam-412	13	2	c	c	X
ejpam-412	13	3	©	©	VERB
ejpam-412	13	4	2009	2009	NUM
ejpam-412	13	5	ejpam	ejpam	NOUN
ejpam-412	13	6	all	all	DET
ejpam-412	13	7	rights	right	NOUN
ejpam-412	13	8	reserved	reserve	VERB
ejpam-412	13	9	.	.	PUNCT
ejpam-412	14	1	i.	i.	PROPN
ejpam-412	14	2	abdel	abdel	PROPN
ejpam-412	14	3	-	-	PUNCT
ejpam-412	14	4	halim	halim	PROPN
ejpam-412	14	5	and	and	CCONJ
ejpam-412	14	6	v.	v.	ADP
ejpam-412	14	7	ertürk	ertürk	PROPN
ejpam-412	14	8	/	/	SYM
ejpam-412	14	9	eur	eur	PROPN
ejpam-412	14	10	.	.	PUNCT
ejpam-412	15	1	j.	j.	PROPN
ejpam-412	15	2	pure	pure	PROPN
ejpam-412	15	3	appl	appl	PROPN
ejpam-412	15	4	.	.	PROPN
ejpam-412	15	5	math	math	PROPN
ejpam-412	15	6	,	,	PUNCT
ejpam-412	15	7	2	2	NUM
ejpam-412	15	8	(	(	PUNCT
ejpam-412	15	9	2009	2009	NUM
ejpam-412	15	10	)	)	PUNCT
ejpam-412	15	11	,	,	PUNCT
ejpam-412	15	12	(	(	PUNCT
ejpam-412	15	13	426	426	NUM
ejpam-412	15	14	-	-	NUM
ejpam-412	15	15	447	447	NUM
ejpam-412	15	16	)	)	PUNCT
ejpam-412	15	17	427	427	NUM
ejpam-412	15	18	key	key	ADJ
ejpam-412	15	19	words	word	NOUN
ejpam-412	15	20	and	and	CCONJ
ejpam-412	15	21	phrases	phrase	NOUN
ejpam-412	15	22	:	:	PUNCT
ejpam-412	15	23	higher	high	ADJ
ejpam-412	15	24	-	-	PUNCT
ejpam-412	15	25	order	order	NOUN
ejpam-412	15	26	boundary	boundary	ADJ
ejpam-412	15	27	value	value	NOUN
ejpam-412	15	28	problem	problem	NOUN
ejpam-412	15	29	,	,	PUNCT
ejpam-412	15	30	differential	differential	ADJ
ejpam-412	15	31	transformation	transformation	NOUN
ejpam-412	15	32	,	,	PUNCT
ejpam-412	15	33	taylor	taylor	PROPN
ejpam-412	15	34	’s	’s	PART
ejpam-412	15	35	series	series	PROPN
ejpam-412	15	36	expansion	expansion	NOUN
ejpam-412	15	37	.	.	PUNCT
ejpam-412	16	1	1	1	X
ejpam-412	16	2	.	.	X
ejpam-412	16	3	introduction	introduction	NOUN
ejpam-412	16	4	recently	recently	ADV
ejpam-412	16	5	a	a	DET
ejpam-412	16	6	great	great	ADJ
ejpam-412	16	7	deal	deal	NOUN
ejpam-412	16	8	of	of	ADP
ejpam-412	16	9	interest	interest	NOUN
ejpam-412	16	10	has	have	AUX
ejpam-412	16	11	been	be	AUX
ejpam-412	16	12	focused	focus	VERB
ejpam-412	16	13	on	on	ADP
ejpam-412	16	14	the	the	DET
ejpam-412	16	15	applications	application	NOUN
ejpam-412	16	16	of	of	ADP
ejpam-412	16	17	the	the	DET
ejpam-412	16	18	(	(	PUNCT
ejpam-412	16	19	dtm	dtm	NOUN
ejpam-412	16	20	)	)	PUNCT
ejpam-412	16	21	to	to	PART
ejpam-412	16	22	solve	solve	VERB
ejpam-412	16	23	various	various	ADJ
ejpam-412	16	24	scientific	scientific	ADJ
ejpam-412	16	25	models	model	NOUN
ejpam-412	16	26	,	,	PUNCT
ejpam-412	16	27	see	see	VERB
ejpam-412	16	28	refs.[2],[3],[4],[5	refs.[2],[3],[4],[5	VERB
ejpam-412	16	29	-	-	PUNCT
ejpam-412	16	30	6],[7	6],[7	NUM
ejpam-412	16	31	-	-	PUNCT
ejpam-412	16	32	8],[9],[13	8],[9],[13	NUM
ejpam-412	16	33	-	-	SYM
ejpam-412	16	34	15	15	NUM
ejpam-412	16	35	]	]	PUNCT
ejpam-412	16	36	,	,	PUNCT
ejpam-412	16	37	[	[	X
ejpam-412	16	38	1617	1617	NUM
ejpam-412	16	39	]	]	PUNCT
ejpam-412	16	40	,	,	PUNCT
ejpam-412	17	1	[	[	X
ejpam-412	17	2	18	18	NUM
ejpam-412	17	3	]	]	PUNCT
ejpam-412	17	4	and	and	CCONJ
ejpam-412	17	5	[	[	X
ejpam-412	17	6	22	22	NUM
ejpam-412	17	7	]	]	PUNCT
ejpam-412	17	8	.	.	PUNCT
ejpam-412	18	1	the	the	DET
ejpam-412	18	2	(	(	PUNCT
ejpam-412	18	3	dtm	dtm	NOUN
ejpam-412	18	4	)	)	PUNCT
ejpam-412	18	5	has	have	AUX
ejpam-412	18	6	also	also	ADV
ejpam-412	18	7	been	be	AUX
ejpam-412	18	8	applied	apply	VERB
ejpam-412	18	9	to	to	PART
ejpam-412	18	10	solve	solve	VERB
ejpam-412	18	11	linear	linear	ADJ
ejpam-412	18	12	and	and	CCONJ
ejpam-412	18	13	non	non	ADJ
ejpam-412	18	14	-	-	ADJ
ejpam-412	18	15	linear	linear	ADJ
ejpam-412	18	16	higher	high	ADJ
ejpam-412	18	17	-	-	PUNCT
ejpam-412	18	18	order	order	NOUN
ejpam-412	18	19	initial	initial	ADJ
ejpam-412	18	20	value	value	NOUN
ejpam-412	18	21	problems	problem	NOUN
ejpam-412	18	22	,	,	PUNCT
ejpam-412	18	23	for	for	ADP
ejpam-412	18	24	example	example	NOUN
ejpam-412	18	25	[	[	X
ejpam-412	18	26	15	15	NUM
ejpam-412	18	27	]	]	PUNCT
ejpam-412	18	28	and	and	CCONJ
ejpam-412	18	29	[	[	X
ejpam-412	18	30	16	16	NUM
ejpam-412	18	31	]	]	PUNCT
ejpam-412	18	32	.	.	PUNCT
ejpam-412	19	1	in	in	ADP
ejpam-412	19	2	this	this	DET
ejpam-412	19	3	paper	paper	NOUN
ejpam-412	19	4	,	,	PUNCT
ejpam-412	19	5	we	we	PRON
ejpam-412	19	6	are	be	AUX
ejpam-412	19	7	interested	interested	ADJ
ejpam-412	19	8	in	in	ADP
ejpam-412	19	9	the	the	DET
ejpam-412	19	10	differential	differential	ADJ
ejpam-412	19	11	transformation	transformation	NOUN
ejpam-412	19	12	method	method	NOUN
ejpam-412	19	13	(	(	PUNCT
ejpam-412	19	14	dtm	dtm	PROPN
ejpam-412	19	15	)	)	PUNCT
ejpam-412	19	16	to	to	PART
ejpam-412	19	17	solve	solve	VERB
ejpam-412	19	18	linear	linear	ADJ
ejpam-412	19	19	and	and	CCONJ
ejpam-412	19	20	non	non	ADJ
ejpam-412	19	21	-	-	ADJ
ejpam-412	19	22	linear	linear	ADJ
ejpam-412	19	23	higher	high	ADJ
ejpam-412	19	24	-	-	PUNCT
ejpam-412	19	25	order	order	NOUN
ejpam-412	19	26	boundary	boundary	ADJ
ejpam-412	19	27	value	value	NOUN
ejpam-412	19	28	problems	problem	NOUN
ejpam-412	19	29	(	(	PUNCT
ejpam-412	19	30	hobvps	hobvps	PROPN
ejpam-412	19	31	)	)	PUNCT
ejpam-412	19	32	.	.	PUNCT
ejpam-412	20	1	many	many	ADJ
ejpam-412	20	2	numerical	numerical	ADJ
ejpam-412	20	3	techniques	technique	NOUN
ejpam-412	20	4	,	,	PUNCT
ejpam-412	20	5	such	such	ADJ
ejpam-412	20	6	as	as	ADP
ejpam-412	20	7	finite	finite	ADJ
ejpam-412	20	8	difference	difference	NOUN
ejpam-412	20	9	method	method	NOUN
ejpam-412	20	10	[	[	X
ejpam-412	20	11	10	10	NUM
ejpam-412	20	12	]	]	PUNCT
ejpam-412	20	13	and	and	CCONJ
ejpam-412	20	14	decomposition	decomposition	NOUN
ejpam-412	20	15	method	method	NOUN
ejpam-412	20	16	[	[	X
ejpam-412	20	17	19	19	NUM
ejpam-412	20	18	-	-	SYM
ejpam-412	20	19	21	21	NUM
ejpam-412	20	20	]	]	PUNCT
ejpam-412	20	21	have	have	AUX
ejpam-412	20	22	been	be	AUX
ejpam-412	20	23	implemented	implement	VERB
ejpam-412	20	24	to	to	PART
ejpam-412	20	25	solve	solve	VERB
ejpam-412	20	26	(	(	PUNCT
ejpam-412	20	27	hobvps	hobvps	NOUN
ejpam-412	20	28	)	)	PUNCT
ejpam-412	20	29	numerically	numerically	ADV
ejpam-412	20	30	.	.	PUNCT
ejpam-412	21	1	the	the	DET
ejpam-412	21	2	differential	differential	ADJ
ejpam-412	21	3	transformation	transformation	NOUN
ejpam-412	21	4	method	method	NOUN
ejpam-412	21	5	(	(	PUNCT
ejpam-412	21	6	dtm	dtm	PROPN
ejpam-412	21	7	)	)	PUNCT
ejpam-412	21	8	is	be	AUX
ejpam-412	21	9	a	a	DET
ejpam-412	21	10	numerical	numerical	ADJ
ejpam-412	21	11	method	method	NOUN
ejpam-412	21	12	for	for	ADP
ejpam-412	21	13	solving	solve	VERB
ejpam-412	21	14	boundary	boundary	ADJ
ejpam-412	21	15	value	value	NOUN
ejpam-412	21	16	problem	problem	NOUN
ejpam-412	21	17	[	[	X
ejpam-412	21	18	17	17	NUM
ejpam-412	21	19	]	]	PUNCT
ejpam-412	21	20	.	.	PUNCT
ejpam-412	22	1	the	the	DET
ejpam-412	22	2	concept	concept	NOUN
ejpam-412	22	3	of	of	ADP
ejpam-412	22	4	differential	differential	ADJ
ejpam-412	22	5	transformation	transformation	NOUN
ejpam-412	22	6	was	be	AUX
ejpam-412	22	7	first	first	ADV
ejpam-412	22	8	proposed	propose	VERB
ejpam-412	22	9	by	by	ADP
ejpam-412	22	10	zhou	zhou	PROPN
ejpam-412	23	1	[	[	X
ejpam-412	23	2	23	23	NUM
ejpam-412	23	3	]	]	PUNCT
ejpam-412	23	4	in	in	ADP
ejpam-412	23	5	1986	1986	NUM
ejpam-412	23	6	,	,	PUNCT
ejpam-412	23	7	and	and	CCONJ
ejpam-412	23	8	it	it	PRON
ejpam-412	23	9	was	be	AUX
ejpam-412	23	10	applied	apply	VERB
ejpam-412	23	11	to	to	PART
ejpam-412	23	12	solve	solve	VERB
ejpam-412	23	13	linear	linear	ADJ
ejpam-412	23	14	and	and	CCONJ
ejpam-412	23	15	non	non	ADJ
ejpam-412	23	16	-	-	ADJ
ejpam-412	23	17	linear	linear	ADJ
ejpam-412	23	18	initial	initial	ADJ
ejpam-412	23	19	value	value	NOUN
ejpam-412	23	20	problems	problem	NOUN
ejpam-412	23	21	in	in	ADP
ejpam-412	23	22	electric	electric	ADJ
ejpam-412	23	23	circuit	circuit	NOUN
ejpam-412	23	24	analysis	analysis	NOUN
ejpam-412	23	25	.	.	PUNCT
ejpam-412	24	1	the	the	DET
ejpam-412	24	2	method	method	NOUN
ejpam-412	24	3	can	can	AUX
ejpam-412	24	4	be	be	AUX
ejpam-412	24	5	used	use	VERB
ejpam-412	24	6	to	to	PART
ejpam-412	24	7	evaluates	evaluate	VERB
ejpam-412	24	8	the	the	DET
ejpam-412	24	9	approximating	approximate	VERB
ejpam-412	24	10	solution	solution	NOUN
ejpam-412	24	11	by	by	ADP
ejpam-412	24	12	the	the	DET
ejpam-412	24	13	finite	finite	PROPN
ejpam-412	24	14	taylor	taylor	PROPN
ejpam-412	24	15	series	series	PROPN
ejpam-412	24	16	and	and	CCONJ
ejpam-412	24	17	by	by	ADP
ejpam-412	24	18	an	an	DET
ejpam-412	24	19	iteration	iteration	NOUN
ejpam-412	24	20	procedure	procedure	NOUN
ejpam-412	24	21	described	describe	VERB
ejpam-412	24	22	by	by	ADP
ejpam-412	24	23	the	the	DET
ejpam-412	24	24	transformed	transform	VERB
ejpam-412	24	25	equations	equation	NOUN
ejpam-412	24	26	obtained	obtain	VERB
ejpam-412	24	27	from	from	ADP
ejpam-412	24	28	the	the	DET
ejpam-412	24	29	original	original	ADJ
ejpam-412	24	30	equation	equation	NOUN
ejpam-412	24	31	using	use	VERB
ejpam-412	24	32	the	the	DET
ejpam-412	24	33	operations	operation	NOUN
ejpam-412	24	34	of	of	ADP
ejpam-412	24	35	differential	differential	ADJ
ejpam-412	24	36	transformation	transformation	NOUN
ejpam-412	24	37	.	.	PUNCT
ejpam-412	25	1	the	the	DET
ejpam-412	25	2	basic	basic	ADJ
ejpam-412	25	3	definitions	definition	NOUN
ejpam-412	25	4	of	of	ADP
ejpam-412	25	5	the	the	DET
ejpam-412	25	6	differential	differential	ADJ
ejpam-412	25	7	transformation	transformation	NOUN
ejpam-412	25	8	are	be	AUX
ejpam-412	25	9	introduced	introduce	VERB
ejpam-412	25	10	in	in	ADP
ejpam-412	25	11	section	section	NOUN
ejpam-412	25	12	2	2	NUM
ejpam-412	25	13	.	.	PUNCT
ejpam-412	26	1	the	the	DET
ejpam-412	26	2	mathematical	mathematical	ADJ
ejpam-412	26	3	background	background	NOUN
ejpam-412	26	4	of	of	ADP
ejpam-412	26	5	the	the	DET
ejpam-412	26	6	higher	high	ADJ
ejpam-412	26	7	-	-	PUNCT
ejpam-412	26	8	order	order	NOUN
ejpam-412	26	9	boundary	boundary	ADJ
ejpam-412	26	10	value	value	NOUN
ejpam-412	26	11	problems	problem	NOUN
ejpam-412	26	12	is	be	AUX
ejpam-412	26	13	described	describe	VERB
ejpam-412	26	14	in	in	ADP
ejpam-412	26	15	section	section	NOUN
ejpam-412	26	16	3	3	NUM
ejpam-412	26	17	.	.	PUNCT
ejpam-412	27	1	analysis	analysis	NOUN
ejpam-412	27	2	of	of	ADP
ejpam-412	27	3	higher	high	ADJ
ejpam-412	27	4	-	-	PUNCT
ejpam-412	27	5	order	order	NOUN
ejpam-412	27	6	boundary	boundary	ADJ
ejpam-412	27	7	value	value	NOUN
ejpam-412	27	8	problems	problem	NOUN
ejpam-412	27	9	is	be	AUX
ejpam-412	27	10	illustrated	illustrate	VERB
ejpam-412	27	11	by	by	ADP
ejpam-412	27	12	differential	differential	ADJ
ejpam-412	27	13	transformation	transformation	NOUN
ejpam-412	27	14	method	method	NOUN
ejpam-412	27	15	(	(	PUNCT
ejpam-412	27	16	dtm	dtm	PROPN
ejpam-412	27	17	)	)	PUNCT
ejpam-412	27	18	in	in	ADP
ejpam-412	27	19	section	section	NOUN
ejpam-412	27	20	4	4	NUM
ejpam-412	27	21	.	.	PUNCT
ejpam-412	28	1	numerical	numerical	ADJ
ejpam-412	28	2	examples	example	NOUN
ejpam-412	28	3	are	be	AUX
ejpam-412	28	4	used	use	VERB
ejpam-412	28	5	to	to	PART
ejpam-412	28	6	illustrate	illustrate	VERB
ejpam-412	28	7	the	the	DET
ejpam-412	28	8	effectiveness	effectiveness	NOUN
ejpam-412	28	9	of	of	ADP
ejpam-412	28	10	the	the	DET
ejpam-412	28	11	proposed	propose	VERB
ejpam-412	28	12	method	method	NOUN
ejpam-412	28	13	in	in	ADP
ejpam-412	28	14	section	section	NOUN
ejpam-412	28	15	5	5	NUM
ejpam-412	28	16	.	.	PUNCT
ejpam-412	28	17	i.	i.	PROPN
ejpam-412	28	18	abdel	abdel	PROPN
ejpam-412	28	19	-	-	PUNCT
ejpam-412	28	20	halim	halim	PROPN
ejpam-412	28	21	and	and	CCONJ
ejpam-412	28	22	v.	v.	ADP
ejpam-412	28	23	ertürk	ertürk	PROPN
ejpam-412	28	24	/	/	SYM
ejpam-412	28	25	eur	eur	PROPN
ejpam-412	28	26	.	.	PUNCT
ejpam-412	29	1	j.	j.	PROPN
ejpam-412	29	2	pure	pure	PROPN
ejpam-412	29	3	appl	appl	PROPN
ejpam-412	29	4	.	.	PROPN
ejpam-412	29	5	math	math	PROPN
ejpam-412	29	6	,	,	PUNCT
ejpam-412	29	7	2	2	NUM
ejpam-412	29	8	(	(	PUNCT
ejpam-412	29	9	2009	2009	NUM
ejpam-412	29	10	)	)	PUNCT
ejpam-412	29	11	,	,	PUNCT
ejpam-412	29	12	(	(	PUNCT
ejpam-412	29	13	426	426	NUM
ejpam-412	29	14	-	-	NUM
ejpam-412	29	15	447	447	NUM
ejpam-412	29	16	)	)	PUNCT
ejpam-412	29	17	428	428	NUM
ejpam-412	29	18	2	2	NUM
ejpam-412	29	19	.	.	PUNCT
ejpam-412	30	1	the	the	DET
ejpam-412	30	2	differential	differential	ADJ
ejpam-412	30	3	transformation	transformation	NOUN
ejpam-412	30	4	method	method	NOUN
ejpam-412	30	5	(	(	PUNCT
ejpam-412	30	6	dtm	dtm	PROPN
ejpam-412	30	7	)	)	PUNCT
ejpam-412	30	8	an	an	DET
ejpam-412	30	9	kthorder	kthorder	NOUN
ejpam-412	30	10	differential	differential	NOUN
ejpam-412	30	11	transformation	transformation	NOUN
ejpam-412	30	12	(	(	PUNCT
ejpam-412	30	13	dt	dt	NOUN
ejpam-412	30	14	)	)	PUNCT
ejpam-412	30	15	of	of	ADP
ejpam-412	30	16	a	a	DET
ejpam-412	30	17	function	function	NOUN
ejpam-412	30	18	y(x	y(x	NOUN
ejpam-412	30	19	)	)	PUNCT
ejpam-412	30	20	=	=	SYM
ejpam-412	30	21	f	f	X
ejpam-412	30	22	(	(	PUNCT
ejpam-412	30	23	x	x	X
ejpam-412	30	24	)	)	PUNCT
ejpam-412	30	25	is	be	AUX
ejpam-412	30	26	defined	define	VERB
ejpam-412	30	27	about	about	ADP
ejpam-412	30	28	a	a	DET
ejpam-412	30	29	point	point	NOUN
ejpam-412	30	30	x	x	PUNCT
ejpam-412	31	1	=	=	SYM
ejpam-412	31	2	x0	x0	PROPN
ejpam-412	31	3	as	as	ADP
ejpam-412	31	4	:	:	PUNCT
ejpam-412	31	5	y	y	PROPN
ejpam-412	31	6	(	(	PUNCT
ejpam-412	31	7	k	k	NOUN
ejpam-412	31	8	)	)	PUNCT
ejpam-412	31	9	=	=	SYM
ejpam-412	31	10	1	1	NUM
ejpam-412	31	11	k	k	NOUN
ejpam-412	31	12	!	!	PUNCT
ejpam-412	31	13	h	h	PROPN
ejpam-412	32	1	dk	dk	PROPN
ejpam-412	32	2	y(x	y(x	PROPN
ejpam-412	32	3	)	)	PUNCT
ejpam-412	33	1	d	d	PROPN
ejpam-412	33	2	xk	xk	PROPN
ejpam-412	33	3	i	i	PRON
ejpam-412	33	4	x	x	PROPN
ejpam-412	33	5	=	=	NOUN
ejpam-412	33	6	x0	x0	PROPN
ejpam-412	33	7	,	,	PUNCT
ejpam-412	33	8	(	(	PUNCT
ejpam-412	33	9	2.1	2.1	NUM
ejpam-412	33	10	)	)	PUNCT
ejpam-412	33	11	where	where	SCONJ
ejpam-412	33	12	k	k	PROPN
ejpam-412	33	13	belongs	belong	VERB
ejpam-412	33	14	to	to	ADP
ejpam-412	33	15	the	the	DET
ejpam-412	33	16	set	set	NOUN
ejpam-412	33	17	of	of	ADP
ejpam-412	33	18	non	non	ADJ
ejpam-412	33	19	-	-	ADJ
ejpam-412	33	20	negative	negative	ADJ
ejpam-412	33	21	integers	integer	NOUN
ejpam-412	33	22	,	,	PUNCT
ejpam-412	33	23	denoted	denote	VERB
ejpam-412	33	24	as	as	ADP
ejpam-412	33	25	the	the	DET
ejpam-412	33	26	k	k	NOUN
ejpam-412	33	27	-	-	NOUN
ejpam-412	33	28	domain	domain	NOUN
ejpam-412	33	29	.	.	PUNCT
ejpam-412	34	1	the	the	DET
ejpam-412	34	2	function	function	NOUN
ejpam-412	34	3	y(x	y(x	PROPN
ejpam-412	34	4	)	)	PUNCT
ejpam-412	34	5	may	may	AUX
ejpam-412	34	6	be	be	AUX
ejpam-412	34	7	expressed	express	VERB
ejpam-412	34	8	in	in	ADP
ejpam-412	34	9	terms	term	NOUN
ejpam-412	34	10	of	of	ADP
ejpam-412	34	11	the	the	DET
ejpam-412	34	12	differential	differential	NOUN
ejpam-412	34	13	transforms	transform	VERB
ejpam-412	34	14	(	(	PUNCT
ejpam-412	34	15	dt	dt	PROPN
ejpam-412	34	16	)	)	PUNCT
ejpam-412	34	17	,	,	PUNCT
ejpam-412	34	18	y	y	PROPN
ejpam-412	34	19	(	(	PUNCT
ejpam-412	34	20	k	k	NOUN
ejpam-412	34	21	)	)	PUNCT
ejpam-412	34	22	as	as	ADP
ejpam-412	34	23	:	:	PUNCT
ejpam-412	34	24	y(x	y(x	X
ejpam-412	34	25	)	)	PUNCT
ejpam-412	34	26	=	=	PUNCT
ejpam-412	34	27	∑∞	∑∞	NOUN
ejpam-412	34	28	k=0	k=0	PROPN
ejpam-412	34	29	h	h	PROPN
ejpam-412	34	30	(	(	PUNCT
ejpam-412	34	31	x−x0	x−x0	X
ejpam-412	34	32	)	)	PUNCT
ejpam-412	35	1	k	k	PROPN
ejpam-412	36	1	k	k	X
ejpam-412	36	2	!	!	PUNCT
ejpam-412	37	1	i	i	PRON
ejpam-412	37	2	y	y	INTJ
ejpam-412	37	3	(	(	PUNCT
ejpam-412	37	4	k	k	NOUN
ejpam-412	37	5	)	)	PUNCT
ejpam-412	37	6	.	.	PUNCT
ejpam-412	38	1	(	(	PUNCT
ejpam-412	38	2	2.2	2.2	NUM
ejpam-412	38	3	)	)	PUNCT
ejpam-412	38	4	upon	upon	SCONJ
ejpam-412	38	5	combining	combine	VERB
ejpam-412	38	6	(	(	PUNCT
ejpam-412	38	7	2.1	2.1	NUM
ejpam-412	38	8	)	)	PUNCT
ejpam-412	38	9	and	and	CCONJ
ejpam-412	38	10	(	(	PUNCT
ejpam-412	38	11	2.2	2.2	NUM
ejpam-412	38	12	)	)	PUNCT
ejpam-412	38	13	,	,	PUNCT
ejpam-412	38	14	we	we	PRON
ejpam-412	38	15	obtain	obtain	VERB
ejpam-412	38	16	y(x	y(x	NOUN
ejpam-412	38	17	)	)	PUNCT
ejpam-412	39	1	=	=	PUNCT
ejpam-412	39	2	∑∞	∑∞	NOUN
ejpam-412	39	3	k=0(x	k=0(x	X
ejpam-412	40	1	−	−	X
ejpam-412	40	2	x0	x0	PROPN
ejpam-412	40	3	)	)	PUNCT
ejpam-412	41	1	k	k	PROPN
ejpam-412	41	2	1	1	NUM
ejpam-412	41	3	k	k	NOUN
ejpam-412	41	4	!	!	PUNCT
ejpam-412	42	1	h	h	PROPN
ejpam-412	43	1	dk	dk	PROPN
ejpam-412	43	2	y(x	y(x	PROPN
ejpam-412	43	3	)	)	PUNCT
ejpam-412	44	1	d	d	PROPN
ejpam-412	44	2	xk	xk	PROPN
ejpam-412	44	3	i	i	PRON
ejpam-412	44	4	x	x	PROPN
ejpam-412	44	5	=	=	NOUN
ejpam-412	44	6	x0	x0	PROPN
ejpam-412	44	7	,	,	PUNCT
ejpam-412	44	8	(	(	PUNCT
ejpam-412	44	9	2.3	2.3	NUM
ejpam-412	44	10	)	)	PUNCT
ejpam-412	44	11	which	which	PRON
ejpam-412	44	12	is	be	AUX
ejpam-412	44	13	actually	actually	ADV
ejpam-412	44	14	the	the	DET
ejpam-412	44	15	taylor	taylor	PROPN
ejpam-412	44	16	’s	’s	PART
ejpam-412	44	17	series	series	NOUN
ejpam-412	44	18	for	for	ADP
ejpam-412	44	19	y(x	y(x	NOUN
ejpam-412	44	20	)	)	PUNCT
ejpam-412	44	21	about	about	ADP
ejpam-412	44	22	x	x	X
ejpam-412	44	23	=	=	SYM
ejpam-412	44	24	x0	x0	PROPN
ejpam-412	44	25	.	.	PUNCT
ejpam-412	45	1	from	from	ADP
ejpam-412	45	2	the	the	DET
ejpam-412	45	3	basic	basic	ADJ
ejpam-412	45	4	definition	definition	NOUN
ejpam-412	45	5	of	of	ADP
ejpam-412	45	6	the	the	DET
ejpam-412	45	7	differential	differential	NOUN
ejpam-412	45	8	transforms	transform	VERB
ejpam-412	45	9	(	(	PUNCT
ejpam-412	45	10	dt	dt	PROPN
ejpam-412	45	11	)	)	PUNCT
ejpam-412	45	12	,	,	PUNCT
ejpam-412	45	13	one	one	PRON
ejpam-412	45	14	can	can	AUX
ejpam-412	45	15	obtain	obtain	VERB
ejpam-412	45	16	certain	certain	ADJ
ejpam-412	45	17	laws	law	NOUN
ejpam-412	45	18	of	of	ADP
ejpam-412	45	19	transformational	transformational	ADJ
ejpam-412	45	20	operations	operation	NOUN
ejpam-412	45	21	,	,	PUNCT
ejpam-412	45	22	some	some	PRON
ejpam-412	45	23	of	of	ADP
ejpam-412	45	24	these	these	PRON
ejpam-412	45	25	,	,	PUNCT
ejpam-412	45	26	are	be	AUX
ejpam-412	45	27	listed	list	VERB
ejpam-412	45	28	in	in	ADP
ejpam-412	45	29	the	the	DET
ejpam-412	45	30	following	following	NOUN
ejpam-412	45	31	.	.	PUNCT
ejpam-412	46	1	(	(	PUNCT
ejpam-412	46	2	1	1	NUM
ejpam-412	46	3	):	):	PUNCT
ejpam-412	46	4	if	if	SCONJ
ejpam-412	46	5	z(x	z(x	NUM
ejpam-412	46	6	)	)	PUNCT
ejpam-412	46	7	=	=	SYM
ejpam-412	46	8	u(x)±	u(x)±	ADJ
ejpam-412	46	9	v(x	v(x	PROPN
ejpam-412	46	10	)	)	PUNCT
ejpam-412	46	11	then	then	ADV
ejpam-412	46	12	,	,	PUNCT
ejpam-412	46	13	z(k	z(k	PROPN
ejpam-412	46	14	)	)	PUNCT
ejpam-412	46	15	=	=	SYM
ejpam-412	46	16	u(k)±	u(k)±	PUNCT
ejpam-412	46	17	v	v	NOUN
ejpam-412	46	18	(	(	PUNCT
ejpam-412	46	19	k	k	NOUN
ejpam-412	46	20	)	)	PUNCT
ejpam-412	46	21	.	.	PUNCT
ejpam-412	47	1	(	(	PUNCT
ejpam-412	47	2	2	2	NUM
ejpam-412	47	3	):	):	PUNCT
ejpam-412	47	4	if	if	SCONJ
ejpam-412	47	5	z(x	z(x	NUM
ejpam-412	47	6	)	)	PUNCT
ejpam-412	47	7	=	=	PUNCT
ejpam-412	47	8	αu(x	αu(x	NOUN
ejpam-412	47	9	)	)	PUNCT
ejpam-412	47	10	then	then	ADV
ejpam-412	47	11	,	,	PUNCT
ejpam-412	47	12	z(k	z(k	PROPN
ejpam-412	47	13	)	)	PUNCT
ejpam-412	47	14	=	=	PUNCT
ejpam-412	47	15	αu(k	αu(k	VERB
ejpam-412	47	16	)	)	PUNCT
ejpam-412	47	17	.	.	PUNCT
ejpam-412	48	1	here	here	ADV
ejpam-412	48	2	α	α	PROPN
ejpam-412	48	3	is	be	AUX
ejpam-412	48	4	a	a	DET
ejpam-412	48	5	constant	constant	ADJ
ejpam-412	48	6	.	.	PUNCT
ejpam-412	49	1	(	(	PUNCT
ejpam-412	49	2	3	3	NUM
ejpam-412	49	3	):	):	PUNCT
ejpam-412	49	4	if	if	SCONJ
ejpam-412	49	5	z(x	z(x	NUM
ejpam-412	49	6	)	)	PUNCT
ejpam-412	49	7	=	=	PUNCT
ejpam-412	49	8	du(x	du(x	X
ejpam-412	49	9	)	)	PUNCT
ejpam-412	50	1	d	d	NOUN
ejpam-412	50	2	x	x	PUNCT
ejpam-412	50	3	then	then	ADV
ejpam-412	50	4	,	,	PUNCT
ejpam-412	50	5	z(k	z(k	PROPN
ejpam-412	50	6	)	)	PUNCT
ejpam-412	50	7	=	=	SYM
ejpam-412	50	8	(	(	PUNCT
ejpam-412	50	9	k+	k+	NOUN
ejpam-412	50	10	1)u(k+	1)u(k+	NUM
ejpam-412	50	11	1	1	NUM
ejpam-412	50	12	)	)	PUNCT
ejpam-412	50	13	.	.	PUNCT
ejpam-412	51	1	(	(	PUNCT
ejpam-412	51	2	4	4	NUM
ejpam-412	51	3	):	):	PUNCT
ejpam-412	51	4	if	if	SCONJ
ejpam-412	51	5	z(x	z(x	NUM
ejpam-412	51	6	)	)	PUNCT
ejpam-412	51	7	=	=	SYM
ejpam-412	51	8	d2u(x	d2u(x	PROPN
ejpam-412	51	9	)	)	PUNCT
ejpam-412	52	1	d	d	NOUN
ejpam-412	52	2	x2	x2	PROPN
ejpam-412	52	3	then	then	ADV
ejpam-412	52	4	,	,	PUNCT
ejpam-412	52	5	z(k	z(k	PROPN
ejpam-412	52	6	)	)	PUNCT
ejpam-412	52	7	=	=	SYM
ejpam-412	52	8	(	(	PUNCT
ejpam-412	52	9	k+	k+	NOUN
ejpam-412	52	10	1)(k+	1)(k+	NUM
ejpam-412	52	11	2)u(k+	2)u(k+	PROPN
ejpam-412	52	12	2	2	NUM
ejpam-412	52	13	)	)	PUNCT
ejpam-412	52	14	.	.	PUNCT
ejpam-412	53	1	(	(	PUNCT
ejpam-412	53	2	5	5	NUM
ejpam-412	53	3	):	):	PUNCT
ejpam-412	53	4	if	if	SCONJ
ejpam-412	53	5	z(x	z(x	NUM
ejpam-412	53	6	)	)	PUNCT
ejpam-412	53	7	=	=	SYM
ejpam-412	53	8	dmu(x	dmu(x	PROPN
ejpam-412	53	9	)	)	PUNCT
ejpam-412	54	1	d	d	NOUN
ejpam-412	54	2	xm	xm	PROPN
ejpam-412	54	3	then	then	ADV
ejpam-412	54	4	,	,	PUNCT
ejpam-412	54	5	z(k	z(k	PROPN
ejpam-412	54	6	)	)	PUNCT
ejpam-412	54	7	=	=	SYM
ejpam-412	54	8	(	(	PUNCT
ejpam-412	54	9	k+	k+	NOUN
ejpam-412	54	10	1)(k+	1)(k+	NUM
ejpam-412	54	11	2	2	NUM
ejpam-412	54	12	)	)	PUNCT
ejpam-412	54	13	·	·	PUNCT
ejpam-412	54	14	·	·	PUNCT
ejpam-412	54	15	·	·	PUNCT
ejpam-412	54	16	(	(	PUNCT
ejpam-412	54	17	k+m)u(k+m	k+m)u(k+m	ADV
ejpam-412	54	18	)	)	PUNCT
ejpam-412	54	19	.	.	PUNCT
ejpam-412	55	1	(	(	PUNCT
ejpam-412	55	2	6	6	NUM
ejpam-412	55	3	):	):	PUNCT
ejpam-412	55	4	if	if	SCONJ
ejpam-412	55	5	z(x	z(x	NUM
ejpam-412	55	6	)	)	PUNCT
ejpam-412	55	7	=	=	SYM
ejpam-412	55	8	u(x)v(x	u(x)v(x	NUM
ejpam-412	55	9	)	)	PUNCT
ejpam-412	55	10	then	then	ADV
ejpam-412	55	11	,	,	PUNCT
ejpam-412	55	12	z(k	z(k	PROPN
ejpam-412	55	13	)	)	PUNCT
ejpam-412	55	14	=	=	PUNCT
ejpam-412	56	1	∑k	∑k	PROPN
ejpam-412	56	2	l=0	l=0	PROPN
ejpam-412	56	3	v	v	NOUN
ejpam-412	56	4	(	(	PUNCT
ejpam-412	56	5	l)u(k−	l)u(k−	X
ejpam-412	56	6	l	l	NOUN
ejpam-412	56	7	)	)	PUNCT
ejpam-412	56	8	.	.	PUNCT
ejpam-412	57	1	(	(	PUNCT
ejpam-412	57	2	7	7	NUM
ejpam-412	57	3	):	):	PUNCT
ejpam-412	57	4	if	if	SCONJ
ejpam-412	57	5	z(x	z(x	NUM
ejpam-412	57	6	)	)	PUNCT
ejpam-412	57	7	=	=	PUNCT
ejpam-412	58	1	x	x	PUNCT
ejpam-412	58	2	m	m	VERB
ejpam-412	58	3	then	then	ADV
ejpam-412	58	4	,	,	PUNCT
ejpam-412	58	5	z(k	z(k	PROPN
ejpam-412	58	6	)	)	PUNCT
ejpam-412	58	7	=	=	SYM
ejpam-412	58	8	δ	δ	PROPN
ejpam-412	58	9	(	(	PUNCT
ejpam-412	58	10	k−	k−	PROPN
ejpam-412	58	11	n)where	n)where	ADV
ejpam-412	58	12	,	,	PUNCT
ejpam-412	58	13	δ	δ	PROPN
ejpam-412	58	14	(	(	PUNCT
ejpam-412	58	15	k−	k−	PROPN
ejpam-412	58	16	n	n	CCONJ
ejpam-412	58	17	)	)	PUNCT
ejpam-412	58	18	=	=	PUNCT
ejpam-412	59	1			PROPN
ejpam-412	59	2			X
ejpam-412	59	3			NOUN
ejpam-412	59	4	1	1	NUM
ejpam-412	59	5	k	k	NOUN
ejpam-412	59	6	=	=	PUNCT
ejpam-412	59	7	n	n	PROPN
ejpam-412	59	8	0	0	NUM
ejpam-412	59	9	k	k	X
ejpam-412	59	10	6=	6=	PROPN
ejpam-412	59	11	n.	n.	PROPN
ejpam-412	59	12	(	(	PUNCT
ejpam-412	59	13	8)	8)	NUM
ejpam-412	59	14	:	:	PUNCT
ejpam-412	59	15	if	if	SCONJ
ejpam-412	59	16	z(x	z(x	NUM
ejpam-412	59	17	)	)	PUNCT
ejpam-412	59	18	=	=	NUM
ejpam-412	59	19	exp(λx	exp(λx	NOUN
ejpam-412	59	20	)	)	PUNCT
ejpam-412	59	21	then	then	ADV
ejpam-412	59	22	,	,	PUNCT
ejpam-412	59	23	z(k	z(k	PROPN
ejpam-412	59	24	)	)	PUNCT
ejpam-412	59	25	=	=	PROPN
ejpam-412	59	26	λk	λk	PROPN
ejpam-412	59	27	k	k	X
ejpam-412	59	28	!	!	PUNCT
ejpam-412	59	29	.	.	PUNCT
ejpam-412	60	1	(	(	PUNCT
ejpam-412	60	2	9	9	NUM
ejpam-412	60	3	):	):	PUNCT
ejpam-412	60	4	if	if	SCONJ
ejpam-412	60	5	z(x	z(x	NUM
ejpam-412	60	6	)	)	PUNCT
ejpam-412	60	7	=	=	SYM
ejpam-412	60	8	(	(	PUNCT
ejpam-412	60	9	1	1	NUM
ejpam-412	60	10	+	+	NUM
ejpam-412	60	11	x)m	x)m	PUNCT
ejpam-412	60	12	then	then	ADV
ejpam-412	60	13	,	,	PUNCT
ejpam-412	60	14	z(k	z(k	PROPN
ejpam-412	60	15	)	)	PUNCT
ejpam-412	60	16	=	=	PUNCT
ejpam-412	60	17	m(m−1)···(m−k+1	m(m−1)···(m−k+1	X
ejpam-412	60	18	)	)	PUNCT
ejpam-412	60	19	k	k	NOUN
ejpam-412	60	20	!	!	PUNCT
ejpam-412	60	21	.	.	PUNCT
ejpam-412	61	1	(	(	PUNCT
ejpam-412	61	2	10	10	NUM
ejpam-412	61	3	):	):	PUNCT
ejpam-412	61	4	if	if	SCONJ
ejpam-412	61	5	z(x	z(x	NUM
ejpam-412	61	6	)	)	PUNCT
ejpam-412	61	7	=	=	NOUN
ejpam-412	61	8	sin(ωx	sin(ωx	X
ejpam-412	61	9	+	+	NOUN
ejpam-412	61	10	α	α	NOUN
ejpam-412	61	11	)	)	PUNCT
ejpam-412	61	12	then	then	ADV
ejpam-412	61	13	,	,	PUNCT
ejpam-412	61	14	z(k	z(k	PROPN
ejpam-412	61	15	)	)	PUNCT
ejpam-412	61	16	=	=	SYM
ejpam-412	61	17	ωk	ωk	ADP
ejpam-412	61	18	k	k	X
ejpam-412	61	19	!	!	NOUN
ejpam-412	61	20	sin(πk	sin(πk	NOUN
ejpam-412	61	21	2	2	NUM
ejpam-412	61	22	+	+	NOUN
ejpam-412	61	23	α	α	NOUN
ejpam-412	61	24	)	)	PUNCT
ejpam-412	61	25	.	.	PUNCT
ejpam-412	62	1	(	(	PUNCT
ejpam-412	62	2	11	11	NUM
ejpam-412	62	3	):	):	PUNCT
ejpam-412	62	4	if	if	SCONJ
ejpam-412	62	5	z(x	z(x	NUM
ejpam-412	62	6	)	)	PUNCT
ejpam-412	62	7	=	=	SYM
ejpam-412	62	8	cos(ωx	cos(ωx	PROPN
ejpam-412	62	9	+	+	NOUN
ejpam-412	62	10	α	α	NOUN
ejpam-412	62	11	)	)	PUNCT
ejpam-412	62	12	then	then	ADV
ejpam-412	62	13	,	,	PUNCT
ejpam-412	62	14	z(k	z(k	PROPN
ejpam-412	62	15	)	)	PUNCT
ejpam-412	62	16	=	=	SYM
ejpam-412	62	17	ωk	ωk	ADP
ejpam-412	62	18	k	k	PROPN
ejpam-412	62	19	!	!	PUNCT
ejpam-412	62	20	cos(πk	cos(πk	NOUN
ejpam-412	62	21	2	2	NUM
ejpam-412	62	22	+	+	NOUN
ejpam-412	62	23	α	α	NOUN
ejpam-412	62	24	)	)	PUNCT
ejpam-412	62	25	.	.	PUNCT
ejpam-412	63	1	i.	i.	PROPN
ejpam-412	63	2	abdel	abdel	PROPN
ejpam-412	63	3	-	-	PUNCT
ejpam-412	63	4	halim	halim	PROPN
ejpam-412	63	5	and	and	CCONJ
ejpam-412	63	6	v.	v.	ADP
ejpam-412	63	7	ertürk	ertürk	PROPN
ejpam-412	63	8	/	/	SYM
ejpam-412	63	9	eur	eur	PROPN
ejpam-412	63	10	.	.	PUNCT
ejpam-412	64	1	j.	j.	PROPN
ejpam-412	64	2	pure	pure	PROPN
ejpam-412	64	3	appl	appl	PROPN
ejpam-412	64	4	.	.	PROPN
ejpam-412	64	5	math	math	PROPN
ejpam-412	64	6	,	,	PUNCT
ejpam-412	64	7	2	2	NUM
ejpam-412	64	8	(	(	PUNCT
ejpam-412	64	9	2009	2009	NUM
ejpam-412	64	10	)	)	PUNCT
ejpam-412	64	11	,	,	PUNCT
ejpam-412	64	12	(	(	PUNCT
ejpam-412	64	13	426	426	NUM
ejpam-412	64	14	-	-	NUM
ejpam-412	64	15	447	447	NUM
ejpam-412	64	16	)	)	PUNCT
ejpam-412	64	17	429	429	NUM
ejpam-412	64	18	3	3	NUM
ejpam-412	64	19	.	.	PUNCT
ejpam-412	65	1	the	the	DET
ejpam-412	65	2	higher	high	ADJ
ejpam-412	65	3	-	-	PUNCT
ejpam-412	65	4	order	order	NOUN
ejpam-412	65	5	boundary	boundary	ADJ
ejpam-412	65	6	value	value	NOUN
ejpam-412	65	7	problems	problem	NOUN
ejpam-412	65	8	(	(	PUNCT
ejpam-412	65	9	i	i	NOUN
ejpam-412	65	10	)	)	PUNCT
ejpam-412	65	11	even	even	ADV
ejpam-412	65	12	-	-	PUNCT
ejpam-412	65	13	order	order	NOUN
ejpam-412	65	14	boundary	boundary	ADJ
ejpam-412	65	15	value	value	NOUN
ejpam-412	65	16	problems	problem	NOUN
ejpam-412	65	17	consider	consider	VERB
ejpam-412	65	18	the	the	DET
ejpam-412	65	19	special	special	ADJ
ejpam-412	65	20	(	(	PUNCT
ejpam-412	65	21	2m)-order	2m)-order	NUM
ejpam-412	65	22	bvp	bvp	NOUN
ejpam-412	65	23	of	of	ADP
ejpam-412	65	24	the	the	DET
ejpam-412	65	25	form	form	NOUN
ejpam-412	65	26	y(2m)(x	y(2m)(x	NOUN
ejpam-412	65	27	)	)	PUNCT
ejpam-412	66	1	=	=	SYM
ejpam-412	66	2	f	f	X
ejpam-412	66	3	(	(	PUNCT
ejpam-412	66	4	x	x	INTJ
ejpam-412	66	5	,	,	PUNCT
ejpam-412	66	6	y	y	PROPN
ejpam-412	66	7	)	)	PUNCT
ejpam-412	66	8	,	,	PUNCT
ejpam-412	66	9	0	0	NUM
ejpam-412	66	10	<	<	X
ejpam-412	66	11	x	x	X
ejpam-412	66	12	<	<	X
ejpam-412	66	13	b	b	PROPN
ejpam-412	66	14	,	,	PUNCT
ejpam-412	66	15	(	(	PUNCT
ejpam-412	66	16	3.1	3.1	NUM
ejpam-412	66	17	)	)	PUNCT
ejpam-412	66	18	with	with	ADP
ejpam-412	66	19	boundary	boundary	ADJ
ejpam-412	66	20	conditions	condition	NOUN
ejpam-412	66	21	y(2	y(2	PROPN
ejpam-412	66	22	j)(0	j)(0	ADJ
ejpam-412	66	23	)	)	PUNCT
ejpam-412	66	24	=	=	VERB
ejpam-412	67	1	α2	α2	PROPN
ejpam-412	67	2	j	j	PROPN
ejpam-412	67	3	;	;	PUNCT
ejpam-412	67	4	j	j	PROPN
ejpam-412	67	5	=	=	SYM
ejpam-412	67	6	0	0	PROPN
ejpam-412	67	7	,	,	PUNCT
ejpam-412	67	8	1	1	NUM
ejpam-412	67	9	,	,	PUNCT
ejpam-412	67	10	2	2	NUM
ejpam-412	67	11	,	,	PUNCT
ejpam-412	67	12	.	.	PUNCT
ejpam-412	67	13	.	.	PUNCT
ejpam-412	67	14	.	.	PUNCT
ejpam-412	68	1	,	,	PUNCT
ejpam-412	68	2	(	(	PUNCT
ejpam-412	68	3	m−	m−	PROPN
ejpam-412	68	4	1	1	NUM
ejpam-412	68	5	)	)	PUNCT
ejpam-412	68	6	,	,	PUNCT
ejpam-412	68	7	(	(	PUNCT
ejpam-412	68	8	3.2	3.2	NUM
ejpam-412	68	9	)	)	PUNCT
ejpam-412	68	10	y(2	y(2	PROPN
ejpam-412	68	11	j)(b	j)(b	PROPN
ejpam-412	68	12	)	)	PUNCT
ejpam-412	68	13	=	=	PUNCT
ejpam-412	68	14	β2	β2	PROPN
ejpam-412	68	15	j	j	PROPN
ejpam-412	68	16	;	;	PUNCT
ejpam-412	68	17	j	j	PROPN
ejpam-412	68	18	=	=	SYM
ejpam-412	68	19	0	0	PROPN
ejpam-412	68	20	,	,	PUNCT
ejpam-412	68	21	1	1	NUM
ejpam-412	68	22	,	,	PUNCT
ejpam-412	68	23	2	2	NUM
ejpam-412	68	24	,	,	PUNCT
ejpam-412	68	25	.	.	PUNCT
ejpam-412	68	26	.	.	PUNCT
ejpam-412	68	27	.	.	PUNCT
ejpam-412	69	1	,	,	PUNCT
ejpam-412	69	2	(	(	PUNCT
ejpam-412	69	3	m−	m−	PROPN
ejpam-412	69	4	1	1	NUM
ejpam-412	69	5	)	)	PUNCT
ejpam-412	69	6	,	,	PUNCT
ejpam-412	69	7	(	(	PUNCT
ejpam-412	69	8	3.3	3.3	NUM
ejpam-412	69	9	)	)	PUNCT
ejpam-412	69	10	(	(	PUNCT
ejpam-412	69	11	ii	ii	NOUN
ejpam-412	69	12	)	)	PUNCT
ejpam-412	69	13	odd	odd	ADJ
ejpam-412	69	14	-	-	PUNCT
ejpam-412	69	15	order	order	NOUN
ejpam-412	69	16	boundary	boundary	ADJ
ejpam-412	69	17	value	value	NOUN
ejpam-412	69	18	problems	problem	NOUN
ejpam-412	69	19	consider	consider	VERB
ejpam-412	69	20	the	the	DET
ejpam-412	69	21	special	special	ADJ
ejpam-412	69	22	(	(	PUNCT
ejpam-412	69	23	2m+	2m+	NUM
ejpam-412	69	24	1)-order	1)-order	NUM
ejpam-412	69	25	bvp	bvp	NOUN
ejpam-412	69	26	of	of	ADP
ejpam-412	69	27	the	the	DET
ejpam-412	69	28	form	form	NOUN
ejpam-412	69	29	y(2m+1)(x	y(2m+1)(x	PROPN
ejpam-412	69	30	)	)	PUNCT
ejpam-412	70	1	=	=	SYM
ejpam-412	70	2	f	f	PROPN
ejpam-412	70	3	(	(	PUNCT
ejpam-412	70	4	x	x	INTJ
ejpam-412	70	5	,	,	PUNCT
ejpam-412	70	6	y	y	PROPN
ejpam-412	70	7	)	)	PUNCT
ejpam-412	70	8	,	,	PUNCT
ejpam-412	70	9	0	0	NUM
ejpam-412	70	10	<	<	X
ejpam-412	70	11	x	x	X
ejpam-412	70	12	<	<	X
ejpam-412	70	13	b	b	PROPN
ejpam-412	70	14	,	,	PUNCT
ejpam-412	70	15	(	(	PUNCT
ejpam-412	70	16	3.4	3.4	NUM
ejpam-412	70	17	)	)	PUNCT
ejpam-412	70	18	with	with	ADP
ejpam-412	70	19	boundary	boundary	ADJ
ejpam-412	70	20	conditions	condition	NOUN
ejpam-412	70	21	y(2	y(2	PROPN
ejpam-412	70	22	j+1)(0	j+1)(0	PROPN
ejpam-412	70	23	)	)	PUNCT
ejpam-412	70	24	=	=	SYM
ejpam-412	71	1	γ2	γ2	PROPN
ejpam-412	71	2	j+1	j+1	PROPN
ejpam-412	71	3	;	;	PUNCT
ejpam-412	71	4	j	j	PROPN
ejpam-412	71	5	=	=	SYM
ejpam-412	71	6	0	0	NUM
ejpam-412	71	7	,	,	PUNCT
ejpam-412	71	8	1	1	NUM
ejpam-412	71	9	,	,	PUNCT
ejpam-412	71	10	2	2	NUM
ejpam-412	71	11	,	,	PUNCT
ejpam-412	71	12	.	.	PUNCT
ejpam-412	71	13	.	.	PUNCT
ejpam-412	71	14	.	.	PUNCT
ejpam-412	72	1	,	,	PUNCT
ejpam-412	72	2	m	m	PRON
ejpam-412	72	3	,	,	PUNCT
ejpam-412	72	4	(	(	PUNCT
ejpam-412	72	5	3.5	3.5	NUM
ejpam-412	72	6	)	)	PUNCT
ejpam-412	72	7	y(2	y(2	PROPN
ejpam-412	72	8	j+1)(b	j+1)(b	PROPN
ejpam-412	72	9	)	)	PUNCT
ejpam-412	72	10	=	=	SYM
ejpam-412	73	1	γ2	γ2	PROPN
ejpam-412	73	2	j+1	j+1	PROPN
ejpam-412	73	3	;	;	PUNCT
ejpam-412	73	4	j	j	PROPN
ejpam-412	73	5	=	=	SYM
ejpam-412	73	6	0	0	NUM
ejpam-412	73	7	,	,	PUNCT
ejpam-412	73	8	1	1	NUM
ejpam-412	73	9	,	,	PUNCT
ejpam-412	73	10	2	2	NUM
ejpam-412	73	11	,	,	PUNCT
ejpam-412	73	12	.	.	PUNCT
ejpam-412	73	13	.	.	PUNCT
ejpam-412	73	14	.	.	PUNCT
ejpam-412	74	1	,	,	PUNCT
ejpam-412	74	2	m	m	PRON
ejpam-412	74	3	,	,	PUNCT
ejpam-412	74	4	(	(	PUNCT
ejpam-412	74	5	3.6	3.6	NUM
ejpam-412	74	6	)	)	PUNCT
ejpam-412	74	7	it	it	PRON
ejpam-412	74	8	is	be	AUX
ejpam-412	74	9	interesting	interesting	ADJ
ejpam-412	74	10	to	to	PART
ejpam-412	74	11	point	point	VERB
ejpam-412	74	12	out	out	ADP
ejpam-412	74	13	that	that	SCONJ
ejpam-412	74	14	y(x	y(x	NOUN
ejpam-412	74	15	)	)	PUNCT
ejpam-412	74	16	and	and	CCONJ
ejpam-412	74	17	f	f	PROPN
ejpam-412	74	18	(	(	PUNCT
ejpam-412	74	19	x	x	INTJ
ejpam-412	74	20	,	,	PUNCT
ejpam-412	74	21	y	y	PROPN
ejpam-412	74	22	)	)	PUNCT
ejpam-412	74	23	are	be	AUX
ejpam-412	74	24	assumed	assume	VERB
ejpam-412	74	25	real	real	ADJ
ejpam-412	74	26	and	and	CCONJ
ejpam-412	74	27	as	as	ADP
ejpam-412	74	28	many	many	ADJ
ejpam-412	74	29	times	time	NOUN
ejpam-412	74	30	differentiable	differentiable	ADJ
ejpam-412	74	31	as	as	SCONJ
ejpam-412	74	32	required	require	VERB
ejpam-412	74	33	for	for	ADP
ejpam-412	74	34	x	x	PROPN
ejpam-412	74	35	∈	∈	PROPN
ejpam-412	75	1	[	[	X
ejpam-412	75	2	0	0	NUM
ejpam-412	75	3	,	,	PUNCT
ejpam-412	75	4	b	b	NOUN
ejpam-412	75	5	]	]	PUNCT
ejpam-412	75	6	and	and	CCONJ
ejpam-412	75	7	α2	α2	PROPN
ejpam-412	75	8	j	j	PROPN
ejpam-412	75	9	and	and	CCONJ
ejpam-412	75	10	β2	β2	PROPN
ejpam-412	75	11	j	j	PROPN
ejpam-412	75	12	,	,	PUNCT
ejpam-412	75	13	j	j	PROPN
ejpam-412	75	14	=	=	SYM
ejpam-412	75	15	0	0	NUM
ejpam-412	75	16	,	,	PUNCT
ejpam-412	75	17	1	1	NUM
ejpam-412	75	18	,	,	PUNCT
ejpam-412	75	19	2	2	NUM
ejpam-412	75	20	,	,	PUNCT
ejpam-412	75	21	.	.	PUNCT
ejpam-412	75	22	.	.	PUNCT
ejpam-412	75	23	.	.	PUNCT
ejpam-412	76	1	(	(	PUNCT
ejpam-412	76	2	m−	m−	PROPN
ejpam-412	76	3	1	1	NUM
ejpam-412	76	4	)	)	PUNCT
ejpam-412	76	5	describe	describe	VERB
ejpam-412	76	6	the	the	DET
ejpam-412	76	7	even	even	ADJ
ejpam-412	76	8	-	-	PUNCT
ejpam-412	76	9	order	order	NOUN
ejpam-412	76	10	are	be	AUX
ejpam-412	76	11	real	real	ADJ
ejpam-412	76	12	finite	finite	ADJ
ejpam-412	76	13	constants	constant	NOUN
ejpam-412	76	14	[	[	X
ejpam-412	76	15	11	11	NUM
ejpam-412	76	16	]	]	PUNCT
ejpam-412	76	17	,	,	PUNCT
ejpam-412	76	18	moreover	moreover	ADV
ejpam-412	76	19	,	,	PUNCT
ejpam-412	76	20	the	the	DET
ejpam-412	76	21	conditions	condition	NOUN
ejpam-412	76	22	α2	α2	PROPN
ejpam-412	76	23	j	j	PROPN
ejpam-412	76	24	,	,	PUNCT
ejpam-412	76	25	j	j	PROPN
ejpam-412	76	26	=	=	SYM
ejpam-412	76	27	0	0	NUM
ejpam-412	76	28	,	,	PUNCT
ejpam-412	76	29	1	1	NUM
ejpam-412	76	30	,	,	PUNCT
ejpam-412	76	31	2	2	NUM
ejpam-412	76	32	,	,	PUNCT
ejpam-412	76	33	.	.	PUNCT
ejpam-412	76	34	.	.	PUNCT
ejpam-412	77	1	.	.	PUNCT
ejpam-412	78	1	,	,	PUNCT
ejpam-412	78	2	(	(	PUNCT
ejpam-412	78	3	m−	m−	PROPN
ejpam-412	78	4	1	1	NUM
ejpam-412	78	5	)	)	PUNCT
ejpam-412	78	6	describe	describe	VERB
ejpam-412	78	7	the	the	DET
ejpam-412	78	8	even	even	ADJ
ejpam-412	78	9	-	-	PUNCT
ejpam-412	78	10	order	order	NOUN
ejpam-412	78	11	derivatives	derivative	NOUN
ejpam-412	78	12	at	at	ADP
ejpam-412	78	13	the	the	DET
ejpam-412	78	14	boundary	boundary	NOUN
ejpam-412	78	15	x	x	X
ejpam-412	78	16	=	=	SYM
ejpam-412	78	17	0	0	NUM
ejpam-412	78	18	,	,	PUNCT
ejpam-412	78	19	while	while	SCONJ
ejpam-412	78	20	γ2	γ2	ADJ
ejpam-412	78	21	j+1	j+1	PRON
ejpam-412	78	22	and	and	CCONJ
ejpam-412	78	23	γ2	γ2	PROPN
ejpam-412	78	24	j+1	j+1	NOUN
ejpam-412	78	25	,	,	PUNCT
ejpam-412	78	26	j	j	PROPN
ejpam-412	78	27	=	=	SYM
ejpam-412	78	28	0	0	NUM
ejpam-412	78	29	,	,	PUNCT
ejpam-412	78	30	1	1	NUM
ejpam-412	78	31	,	,	PUNCT
ejpam-412	78	32	2	2	NUM
ejpam-412	78	33	,	,	PUNCT
ejpam-412	78	34	.	.	PUNCT
ejpam-412	78	35	.	.	PUNCT
ejpam-412	79	1	.	.	PUNCT
ejpam-412	80	1	,	,	PUNCT
ejpam-412	80	2	m	m	VERB
ejpam-412	80	3	describe	describe	VERB
ejpam-412	80	4	the	the	DET
ejpam-412	80	5	odd	odd	ADJ
ejpam-412	80	6	-	-	PUNCT
ejpam-412	80	7	order	order	NOUN
ejpam-412	80	8	are	be	AUX
ejpam-412	80	9	real	real	ADJ
ejpam-412	80	10	finite	finite	ADJ
ejpam-412	80	11	constants	constant	NOUN
ejpam-412	80	12	and	and	CCONJ
ejpam-412	80	13	the	the	DET
ejpam-412	80	14	conditions	condition	NOUN
ejpam-412	80	15	γ2	γ2	PROPN
ejpam-412	80	16	j+1	j+1	PROPN
ejpam-412	80	17	,	,	PUNCT
ejpam-412	80	18	j	j	PROPN
ejpam-412	80	19	=	=	SYM
ejpam-412	80	20	0	0	NUM
ejpam-412	80	21	,	,	PUNCT
ejpam-412	80	22	1	1	NUM
ejpam-412	80	23	,	,	PUNCT
ejpam-412	80	24	2	2	NUM
ejpam-412	80	25	,	,	PUNCT
ejpam-412	80	26	.	.	PUNCT
ejpam-412	80	27	.	.	PUNCT
ejpam-412	80	28	.	.	PUNCT
ejpam-412	81	1	m	m	PROPN
ejpam-412	81	2	describe	describe	VERB
ejpam-412	81	3	the	the	DET
ejpam-412	81	4	odd	odd	ADJ
ejpam-412	81	5	-	-	PUNCT
ejpam-412	81	6	order	order	NOUN
ejpam-412	81	7	derivatives	derivative	NOUN
ejpam-412	81	8	at	at	ADP
ejpam-412	81	9	the	the	DET
ejpam-412	81	10	boundary	boundary	NOUN
ejpam-412	81	11	x	x	X
ejpam-412	81	12	=	=	PUNCT
ejpam-412	81	13	b.	b.	PROPN
ejpam-412	81	14	theorems	theorem	NOUN
ejpam-412	81	15	which	which	PRON
ejpam-412	81	16	list	list	VERB
ejpam-412	81	17	the	the	DET
ejpam-412	81	18	conditions	condition	NOUN
ejpam-412	81	19	for	for	ADP
ejpam-412	81	20	existence	existence	NOUN
ejpam-412	81	21	and	and	CCONJ
ejpam-412	81	22	uniqueness	uniqueness	ADJ
ejpam-412	81	23	solution	solution	NOUN
ejpam-412	81	24	of	of	ADP
ejpam-412	81	25	such	such	ADJ
ejpam-412	81	26	problems	problem	NOUN
ejpam-412	81	27	are	be	AUX
ejpam-412	81	28	contained	contain	VERB
ejpam-412	81	29	in	in	ADP
ejpam-412	81	30	a	a	DET
ejpam-412	81	31	comprehensive	comprehensive	ADJ
ejpam-412	81	32	survey	survey	NOUN
ejpam-412	81	33	in	in	ADP
ejpam-412	81	34	a	a	DET
ejpam-412	81	35	book	book	NOUN
ejpam-412	81	36	by	by	ADP
ejpam-412	81	37	agarwal	agarwal	PROPN
ejpam-412	82	1	[	[	X
ejpam-412	82	2	1	1	NUM
ejpam-412	82	3	]	]	PUNCT
ejpam-412	82	4	,	,	PUNCT
ejpam-412	82	5	though	though	SCONJ
ejpam-412	82	6	no	no	DET
ejpam-412	82	7	numerical	numerical	ADJ
ejpam-412	82	8	methods	method	NOUN
ejpam-412	82	9	are	be	AUX
ejpam-412	82	10	contained	contain	VERB
ejpam-412	82	11	therein	therein	ADV
ejpam-412	82	12	for	for	ADP
ejpam-412	82	13	solving	solve	VERB
ejpam-412	82	14	hobvp	hobvp	NOUN
ejpam-412	82	15	’s	’s	ADV
ejpam-412	82	16	of	of	ADP
ejpam-412	82	17	higher	high	ADJ
ejpam-412	82	18	order	order	NOUN
ejpam-412	82	19	.	.	PUNCT
ejpam-412	83	1	i.	i.	PROPN
ejpam-412	83	2	abdel	abdel	PROPN
ejpam-412	83	3	-	-	PUNCT
ejpam-412	83	4	halim	halim	PROPN
ejpam-412	83	5	and	and	CCONJ
ejpam-412	83	6	v.	v.	ADP
ejpam-412	83	7	ertürk	ertürk	PROPN
ejpam-412	83	8	/	/	SYM
ejpam-412	83	9	eur	eur	PROPN
ejpam-412	83	10	.	.	PUNCT
ejpam-412	84	1	j.	j.	PROPN
ejpam-412	84	2	pure	pure	PROPN
ejpam-412	84	3	appl	appl	PROPN
ejpam-412	84	4	.	.	PROPN
ejpam-412	84	5	math	math	PROPN
ejpam-412	84	6	,	,	PUNCT
ejpam-412	84	7	2	2	NUM
ejpam-412	84	8	(	(	PUNCT
ejpam-412	84	9	2009	2009	NUM
ejpam-412	84	10	)	)	PUNCT
ejpam-412	84	11	,	,	PUNCT
ejpam-412	84	12	(	(	PUNCT
ejpam-412	84	13	426	426	NUM
ejpam-412	84	14	-	-	NUM
ejpam-412	84	15	447	447	NUM
ejpam-412	84	16	)	)	PUNCT
ejpam-412	84	17	430	430	NUM
ejpam-412	84	18	4	4	NUM
ejpam-412	84	19	.	.	PUNCT
ejpam-412	85	1	analysis	analysis	NOUN
ejpam-412	85	2	of	of	ADP
ejpam-412	85	3	higher	high	ADJ
ejpam-412	85	4	-	-	PUNCT
ejpam-412	85	5	order	order	NOUN
ejpam-412	85	6	boundary	boundary	ADJ
ejpam-412	85	7	value	value	NOUN
ejpam-412	85	8	problems	problem	NOUN
ejpam-412	85	9	by	by	ADP
ejpam-412	85	10	differential	differential	ADJ
ejpam-412	85	11	transformation	transformation	NOUN
ejpam-412	85	12	let	let	VERB
ejpam-412	85	13	the	the	DET
ejpam-412	85	14	differential	differential	ADJ
ejpam-412	85	15	transform	transform	NOUN
ejpam-412	85	16	of	of	ADP
ejpam-412	85	17	the	the	DET
ejpam-412	85	18	deflection	deflection	NOUN
ejpam-412	85	19	function	function	NOUN
ejpam-412	85	20	y(x	y(x	PROPN
ejpam-412	85	21	)	)	PUNCT
ejpam-412	85	22	be	be	AUX
ejpam-412	85	23	defined	define	VERB
ejpam-412	85	24	from	from	ADP
ejpam-412	85	25	eq	eq	PROPN
ejpam-412	85	26	.	.	PUNCT
ejpam-412	86	1	(	(	PUNCT
ejpam-412	86	2	2.1	2.1	NUM
ejpam-412	86	3	)	)	PUNCT
ejpam-412	86	4	as	as	ADP
ejpam-412	86	5	:	:	PUNCT
ejpam-412	86	6	y	y	PROPN
ejpam-412	86	7	(	(	PUNCT
ejpam-412	86	8	k	k	NOUN
ejpam-412	86	9	)	)	PUNCT
ejpam-412	86	10	=	=	SYM
ejpam-412	87	1	1	1	NUM
ejpam-412	87	2	k	k	NOUN
ejpam-412	87	3	!	!	PUNCT
ejpam-412	87	4	h	h	PROPN
ejpam-412	88	1	dk	dk	PROPN
ejpam-412	88	2	y(x	y(x	PROPN
ejpam-412	88	3	)	)	PUNCT
ejpam-412	89	1	d	d	PROPN
ejpam-412	89	2	xk	xk	PROPN
ejpam-412	89	3	i	i	PRON
ejpam-412	89	4	x	x	PROPN
ejpam-412	89	5	=	=	NOUN
ejpam-412	89	6	x0	x0	PROPN
ejpam-412	89	7	,	,	PUNCT
ejpam-412	89	8	(	(	PUNCT
ejpam-412	89	9	4.1	4.1	NUM
ejpam-412	89	10	)	)	PUNCT
ejpam-412	90	1	where	where	SCONJ
ejpam-412	90	2	x0	x0	PROPN
ejpam-412	90	3	=	=	PUNCT
ejpam-412	91	1	0	0	X
ejpam-412	91	2	.	.	PUNCT
ejpam-412	92	1	also	also	ADV
ejpam-412	92	2	the	the	DET
ejpam-412	92	3	deflection	deflection	NOUN
ejpam-412	92	4	function	function	NOUN
ejpam-412	92	5	may	may	AUX
ejpam-412	92	6	be	be	AUX
ejpam-412	92	7	expressed	express	VERB
ejpam-412	92	8	in	in	ADP
ejpam-412	92	9	terms	term	NOUN
ejpam-412	92	10	of	of	ADP
ejpam-412	92	11	y	y	PROPN
ejpam-412	92	12	(	(	PUNCT
ejpam-412	92	13	k	k	PROPN
ejpam-412	92	14	)	)	PUNCT
ejpam-412	92	15	from	from	ADP
ejpam-412	92	16	eq	eq	ADP
ejpam-412	92	17	.	.	PUNCT
ejpam-412	93	1	(	(	PUNCT
ejpam-412	93	2	2.2	2.2	NUM
ejpam-412	93	3	)	)	PUNCT
ejpam-412	93	4	as	as	ADP
ejpam-412	93	5	:	:	PUNCT
ejpam-412	93	6	y(x	y(x	X
ejpam-412	93	7	)	)	PUNCT
ejpam-412	93	8	=	=	NOUN
ejpam-412	93	9	∑∞	∑∞	NOUN
ejpam-412	93	10	k=0	k=0	PROPN
ejpam-412	93	11	h	h	PROPN
ejpam-412	93	12	xk	xk	PROPN
ejpam-412	94	1	k	k	PROPN
ejpam-412	94	2	!	!	PUNCT
ejpam-412	95	1	i	i	PRON
ejpam-412	95	2	y	y	INTJ
ejpam-412	95	3	(	(	PUNCT
ejpam-412	95	4	k	k	NOUN
ejpam-412	95	5	)	)	PUNCT
ejpam-412	95	6	.	.	PUNCT
ejpam-412	96	1	(	(	PUNCT
ejpam-412	96	2	4.2	4.2	NUM
ejpam-412	96	3	)	)	PUNCT
ejpam-412	96	4	now	now	ADV
ejpam-412	96	5	,	,	PUNCT
ejpam-412	96	6	using	use	VERB
ejpam-412	96	7	the	the	DET
ejpam-412	96	8	transformational	transformational	ADJ
ejpam-412	96	9	operations	operation	NOUN
ejpam-412	96	10	which	which	PRON
ejpam-412	96	11	has	have	AUX
ejpam-412	96	12	been	be	AUX
ejpam-412	96	13	formed	form	VERB
ejpam-412	96	14	in	in	ADP
ejpam-412	96	15	sec.2	sec.2	PROPN
ejpam-412	96	16	,	,	PUNCT
ejpam-412	96	17	one	one	PRON
ejpam-412	96	18	can	can	AUX
ejpam-412	96	19	obtain	obtain	VERB
ejpam-412	96	20	by	by	ADP
ejpam-412	96	21	taking	take	VERB
ejpam-412	96	22	the	the	DET
ejpam-412	96	23	differential	differential	ADJ
ejpam-412	96	24	transform	transform	NOUN
ejpam-412	96	25	of	of	ADP
ejpam-412	96	26	eq	eq	NOUN
ejpam-412	96	27	.	.	PUNCT
ejpam-412	97	1	(	(	PUNCT
ejpam-412	97	2	3.1	3.1	NUM
ejpam-412	97	3	)	)	PUNCT
ejpam-412	97	4	and	and	CCONJ
ejpam-412	97	5	(	(	PUNCT
ejpam-412	97	6	3.4	3.4	NUM
ejpam-412	97	7	)	)	PUNCT
ejpam-412	97	8	respectively	respectively	ADV
ejpam-412	97	9	and	and	CCONJ
ejpam-412	97	10	some	some	DET
ejpam-412	97	11	simplification	simplification	NOUN
ejpam-412	97	12	,	,	PUNCT
ejpam-412	97	13	the	the	DET
ejpam-412	97	14	following	follow	VERB
ejpam-412	97	15	recurrence	recurrence	NOUN
ejpam-412	97	16	equations	equation	NOUN
ejpam-412	97	17	as	as	ADP
ejpam-412	97	18	m=	m=	X
ejpam-412	97	19	0	0	NUM
ejpam-412	97	20	,	,	PUNCT
ejpam-412	97	21	1	1	NUM
ejpam-412	97	22	,	,	PUNCT
ejpam-412	97	23	2	2	NUM
ejpam-412	97	24	,	,	PUNCT
ejpam-412	97	25	.	.	PUNCT
ejpam-412	97	26	.	.	PUNCT
ejpam-412	98	1	..	..	PUNCT
ejpam-412	99	1	y	y	X
ejpam-412	99	2	(	(	PUNCT
ejpam-412	99	3	2m+	2m+	NUM
ejpam-412	99	4	k	k	NOUN
ejpam-412	99	5	)	)	PUNCT
ejpam-412	99	6	=	=	NOUN
ejpam-412	99	7	∑∞	∑∞	NOUN
ejpam-412	99	8	k=0	k=0	PROPN
ejpam-412	99	9	h	h	PROPN
ejpam-412	99	10	(	(	PUNCT
ejpam-412	99	11	2	2	NUM
ejpam-412	99	12	m	m	NOUN
ejpam-412	99	13	)	)	PUNCT
ejpam-412	99	14	!	!	PUNCT
ejpam-412	100	1	(	(	PUNCT
ejpam-412	100	2	2m+k	2m+k	NUM
ejpam-412	100	3	)	)	PUNCT
ejpam-412	100	4	!	!	PUNCT
ejpam-412	101	1	i	i	PRON
ejpam-412	101	2	y	y	INTJ
ejpam-412	101	3	(	(	PUNCT
ejpam-412	101	4	.	.	PUNCT
ejpam-412	101	5	,	,	PUNCT
ejpam-412	101	6	.	.	PUNCT
ejpam-412	101	7	)	)	PUNCT
ejpam-412	101	8	,	,	PUNCT
ejpam-412	101	9	(	(	PUNCT
ejpam-412	101	10	4.3	4.3	NUM
ejpam-412	101	11	)	)	PUNCT
ejpam-412	101	12	y	y	PROPN
ejpam-412	101	13	(	(	PUNCT
ejpam-412	101	14	2m+	2m+	NUM
ejpam-412	101	15	k+	k+	NOUN
ejpam-412	101	16	1	1	NUM
ejpam-412	101	17	)	)	PUNCT
ejpam-412	101	18	=	=	NOUN
ejpam-412	101	19	∑∞	∑∞	NOUN
ejpam-412	101	20	k=0	k=0	PROPN
ejpam-412	101	21	h	h	PROPN
ejpam-412	101	22	(	(	PUNCT
ejpam-412	101	23	2m+1	2m+1	PROPN
ejpam-412	101	24	)	)	PUNCT
ejpam-412	101	25	!	!	PUNCT
ejpam-412	102	1	(	(	PUNCT
ejpam-412	102	2	2m+k+1	2m+k+1	NUM
ejpam-412	102	3	)	)	PUNCT
ejpam-412	102	4	!	!	PUNCT
ejpam-412	103	1	i	i	PRON
ejpam-412	103	2	y	y	INTJ
ejpam-412	103	3	(	(	PUNCT
ejpam-412	103	4	.	.	PUNCT
ejpam-412	103	5	,	,	PUNCT
ejpam-412	103	6	.	.	PUNCT
ejpam-412	103	7	)	)	PUNCT
ejpam-412	103	8	,	,	PUNCT
ejpam-412	103	9	(	(	PUNCT
ejpam-412	103	10	4.4	4.4	NUM
ejpam-412	103	11	)	)	PUNCT
ejpam-412	103	12	where	where	SCONJ
ejpam-412	103	13	y	y	PROPN
ejpam-412	103	14	(	(	PUNCT
ejpam-412	103	15	.	.	PUNCT
ejpam-412	103	16	,	,	PUNCT
ejpam-412	103	17	.	.	PUNCT
ejpam-412	103	18	)	)	PUNCT
ejpam-412	104	1	denotes	denote	VERB
ejpam-412	104	2	the	the	DET
ejpam-412	104	3	transformed	transform	VERB
ejpam-412	104	4	function	function	NOUN
ejpam-412	104	5	of	of	ADP
ejpam-412	104	6	linear	linear	PROPN
ejpam-412	104	7	or	or	CCONJ
ejpam-412	104	8	nonlinear	nonlinear	ADJ
ejpam-412	104	9	function	function	NOUN
ejpam-412	104	10	f	f	PROPN
ejpam-412	104	11	(	(	PUNCT
ejpam-412	104	12	x	x	INTJ
ejpam-412	104	13	,	,	PUNCT
ejpam-412	104	14	y	y	PROPN
ejpam-412	104	15	)	)	PUNCT
ejpam-412	104	16	.	.	PUNCT
ejpam-412	105	1	it	it	PRON
ejpam-412	105	2	may	may	AUX
ejpam-412	105	3	be	be	AUX
ejpam-412	105	4	noted	note	VERB
ejpam-412	105	5	that	that	SCONJ
ejpam-412	105	6	eq	eq	ADP
ejpam-412	105	7	.	.	PUNCT
ejpam-412	106	1	(	(	PUNCT
ejpam-412	106	2	4.2	4.2	NUM
ejpam-412	106	3	)	)	PUNCT
ejpam-412	106	4	is	be	AUX
ejpam-412	106	5	independent	independent	ADJ
ejpam-412	106	6	of	of	ADP
ejpam-412	106	7	the	the	DET
ejpam-412	106	8	boundary	boundary	ADJ
ejpam-412	106	9	conditions	condition	NOUN
ejpam-412	106	10	.	.	PUNCT
ejpam-412	107	1	the	the	DET
ejpam-412	107	2	differential	differential	NOUN
ejpam-412	107	3	transforms	transform	VERB
ejpam-412	107	4	of	of	ADP
ejpam-412	107	5	the	the	DET
ejpam-412	107	6	boundary	boundary	ADJ
ejpam-412	107	7	conditions	condition	NOUN
ejpam-412	107	8	at	at	ADP
ejpam-412	107	9	x	x	X
ejpam-412	107	10	=	=	SYM
ejpam-412	107	11	0	0	NUM
ejpam-412	107	12	are	be	AUX
ejpam-412	107	13	obtained	obtain	VERB
ejpam-412	107	14	from	from	ADP
ejpam-412	107	15	eqs	eqs	PROPN
ejpam-412	107	16	.	.	PUNCT
ejpam-412	108	1	(	(	PUNCT
ejpam-412	108	2	3.2	3.2	NUM
ejpam-412	108	3	)	)	PUNCT
ejpam-412	108	4	and	and	CCONJ
ejpam-412	108	5	(	(	PUNCT
ejpam-412	108	6	3.5	3.5	NUM
ejpam-412	108	7	)	)	PUNCT
ejpam-412	108	8	in	in	ADP
ejpam-412	108	9	the	the	DET
ejpam-412	108	10	cases	case	NOUN
ejpam-412	108	11	even	even	ADV
ejpam-412	108	12	-	-	PUNCT
ejpam-412	108	13	order	order	NOUN
ejpam-412	108	14	(	(	PUNCT
ejpam-412	108	15	odd	odd	ADJ
ejpam-412	108	16	-	-	PUNCT
ejpam-412	108	17	order	order	NOUN
ejpam-412	108	18	)	)	PUNCT
ejpam-412	108	19	boundary	boundary	ADJ
ejpam-412	108	20	value	value	NOUN
ejpam-412	108	21	problems	problem	NOUN
ejpam-412	108	22	respectively	respectively	ADV
ejpam-412	108	23	,	,	PUNCT
ejpam-412	108	24	with	with	ADP
ejpam-412	108	25	the	the	DET
ejpam-412	108	26	definition	definition	NOUN
ejpam-412	108	27	(	(	PUNCT
ejpam-412	108	28	4.1	4.1	NUM
ejpam-412	108	29	)	)	PUNCT
ejpam-412	108	30	as	as	ADP
ejpam-412	108	31	:	:	PUNCT
ejpam-412	108	32	y	y	PROPN
ejpam-412	108	33	(	(	PUNCT
ejpam-412	108	34	2	2	NUM
ejpam-412	108	35	j	j	NOUN
ejpam-412	108	36	)	)	PUNCT
ejpam-412	108	37	=	=	SYM
ejpam-412	109	1	1	1	NUM
ejpam-412	109	2	(	(	PUNCT
ejpam-412	109	3	2	2	NUM
ejpam-412	109	4	j	j	NOUN
ejpam-412	109	5	)	)	PUNCT
ejpam-412	109	6	!	!	PUNCT
ejpam-412	110	1	α2	α2	PROPN
ejpam-412	110	2	j	j	PROPN
ejpam-412	110	3	,	,	PUNCT
ejpam-412	110	4	j	j	PROPN
ejpam-412	110	5	=	=	SYM
ejpam-412	110	6	0	0	NUM
ejpam-412	110	7	,	,	PUNCT
ejpam-412	110	8	1	1	NUM
ejpam-412	110	9	,	,	PUNCT
ejpam-412	110	10	2	2	NUM
ejpam-412	110	11	,	,	PUNCT
ejpam-412	110	12	.	.	PUNCT
ejpam-412	110	13	.	.	PUNCT
ejpam-412	110	14	.	.	PUNCT
ejpam-412	111	1	,	,	PUNCT
ejpam-412	111	2	(	(	PUNCT
ejpam-412	111	3	2m−	2m−	NOUN
ejpam-412	111	4	1	1	NUM
ejpam-412	111	5	)	)	PUNCT
ejpam-412	111	6	,	,	PUNCT
ejpam-412	111	7	(	(	PUNCT
ejpam-412	111	8	4.5	4.5	X
ejpam-412	111	9	)	)	PUNCT
ejpam-412	111	10	y	y	PROPN
ejpam-412	111	11	(	(	PUNCT
ejpam-412	111	12	2	2	NUM
ejpam-412	111	13	j+	j+	NUM
ejpam-412	111	14	1	1	NUM
ejpam-412	111	15	)	)	PUNCT
ejpam-412	111	16	=	=	SYM
ejpam-412	111	17	1	1	NUM
ejpam-412	111	18	(	(	PUNCT
ejpam-412	111	19	2	2	NUM
ejpam-412	111	20	j+1	j+1	NUM
ejpam-412	111	21	)	)	PUNCT
ejpam-412	111	22	!	!	PUNCT
ejpam-412	112	1	γ2	γ2	PROPN
ejpam-412	112	2	j+1	j+1	PROPN
ejpam-412	112	3	,	,	PUNCT
ejpam-412	112	4	j	j	PROPN
ejpam-412	112	5	=	=	SYM
ejpam-412	112	6	0	0	NUM
ejpam-412	112	7	,	,	PUNCT
ejpam-412	112	8	1	1	NUM
ejpam-412	112	9	,	,	PUNCT
ejpam-412	112	10	2	2	NUM
ejpam-412	112	11	,	,	PUNCT
ejpam-412	112	12	.	.	PUNCT
ejpam-412	112	13	.	.	PUNCT
ejpam-412	112	14	.	.	PUNCT
ejpam-412	113	1	,	,	PUNCT
ejpam-412	113	2	2	2	NUM
ejpam-412	113	3	m	m	NOUN
ejpam-412	113	4	,	,	PUNCT
ejpam-412	113	5	(	(	PUNCT
ejpam-412	113	6	4.6	4.6	NUM
ejpam-412	113	7	)	)	PUNCT
ejpam-412	113	8	substituting	substitute	VERB
ejpam-412	113	9	from	from	ADP
ejpam-412	113	10	(	(	PUNCT
ejpam-412	113	11	4.5	4.5	NUM
ejpam-412	113	12	)	)	PUNCT
ejpam-412	113	13	and	and	CCONJ
ejpam-412	113	14	(	(	PUNCT
ejpam-412	113	15	4.6	4.6	NUM
ejpam-412	113	16	)	)	PUNCT
ejpam-412	113	17	into	into	ADP
ejpam-412	113	18	(	(	PUNCT
ejpam-412	113	19	4.3	4.3	NUM
ejpam-412	113	20	)	)	PUNCT
ejpam-412	113	21	or	or	CCONJ
ejpam-412	113	22	(	(	PUNCT
ejpam-412	113	23	4.4	4.4	NUM
ejpam-412	113	24	)	)	PUNCT
ejpam-412	113	25	and	and	CCONJ
ejpam-412	113	26	using	use	VERB
ejpam-412	113	27	(	(	PUNCT
ejpam-412	113	28	4.2	4.2	NUM
ejpam-412	113	29	)	)	PUNCT
ejpam-412	113	30	,	,	PUNCT
ejpam-412	113	31	yields	yield	NOUN
ejpam-412	113	32	for	for	ADP
ejpam-412	113	33	j	j	PROPN
ejpam-412	113	34	=	=	SYM
ejpam-412	113	35	0	0	PROPN
ejpam-412	113	36	,	,	PUNCT
ejpam-412	113	37	1	1	NUM
ejpam-412	113	38	,	,	PUNCT
ejpam-412	113	39	2	2	NUM
ejpam-412	113	40	,	,	PUNCT
ejpam-412	113	41	.	.	PUNCT
ejpam-412	113	42	.	.	PUNCT
ejpam-412	113	43	.	.	PUNCT
ejpam-412	114	1	,	,	PUNCT
ejpam-412	114	2	(	(	PUNCT
ejpam-412	114	3	m−	m−	PROPN
ejpam-412	114	4	1	1	NUM
ejpam-412	114	5	)	)	PUNCT
ejpam-412	114	6	,	,	PUNCT
ejpam-412	114	7	y(x	y(x	PROPN
ejpam-412	114	8	)	)	PUNCT
ejpam-412	114	9	=	=	NOUN
ejpam-412	114	10	∑∞	∑∞	NOUN
ejpam-412	114	11	k=0	k=0	PROPN
ejpam-412	114	12	h	h	NOUN
ejpam-412	114	13	1	1	NUM
ejpam-412	114	14	(	(	PUNCT
ejpam-412	114	15	2	2	NUM
ejpam-412	114	16	j	j	NOUN
ejpam-412	114	17	)	)	PUNCT
ejpam-412	114	18	!	!	PUNCT
ejpam-412	115	1	α2	α2	PROPN
ejpam-412	116	1	j	j	PROPN
ejpam-412	117	1	i	i	PRON
ejpam-412	117	2	y	y	PROPN
ejpam-412	117	3	(	(	PUNCT
ejpam-412	117	4	k)x	k)x	X
ejpam-412	117	5	k	k	X
ejpam-412	117	6	,	,	PUNCT
ejpam-412	117	7	(	(	PUNCT
ejpam-412	117	8	4.7	4.7	NUM
ejpam-412	117	9	)	)	PUNCT
ejpam-412	117	10	i.	i.	PROPN
ejpam-412	117	11	abdel	abdel	PROPN
ejpam-412	117	12	-	-	PUNCT
ejpam-412	117	13	halim	halim	PROPN
ejpam-412	117	14	and	and	CCONJ
ejpam-412	117	15	v.	v.	ADP
ejpam-412	117	16	ertürk	ertürk	PROPN
ejpam-412	117	17	/	/	SYM
ejpam-412	117	18	eur	eur	PROPN
ejpam-412	117	19	.	.	PUNCT
ejpam-412	118	1	j.	j.	PROPN
ejpam-412	118	2	pure	pure	PROPN
ejpam-412	118	3	appl	appl	PROPN
ejpam-412	118	4	.	.	PROPN
ejpam-412	118	5	math	math	PROPN
ejpam-412	118	6	,	,	PUNCT
ejpam-412	118	7	2	2	NUM
ejpam-412	118	8	(	(	PUNCT
ejpam-412	118	9	2009	2009	NUM
ejpam-412	118	10	)	)	PUNCT
ejpam-412	118	11	,	,	PUNCT
ejpam-412	118	12	(	(	PUNCT
ejpam-412	118	13	426	426	NUM
ejpam-412	118	14	-	-	NUM
ejpam-412	118	15	447	447	NUM
ejpam-412	118	16	)	)	PUNCT
ejpam-412	118	17	431	431	NUM
ejpam-412	118	18	and	and	CCONJ
ejpam-412	118	19	for	for	ADP
ejpam-412	118	20	j	j	PROPN
ejpam-412	118	21	=	=	SYM
ejpam-412	118	22	0	0	PROPN
ejpam-412	118	23	,	,	PUNCT
ejpam-412	118	24	1	1	NUM
ejpam-412	118	25	,	,	PUNCT
ejpam-412	118	26	2	2	NUM
ejpam-412	118	27	,	,	PUNCT
ejpam-412	118	28	.	.	PUNCT
ejpam-412	118	29	.	.	PUNCT
ejpam-412	118	30	.	.	PUNCT
ejpam-412	119	1	,	,	PUNCT
ejpam-412	119	2	m	m	PROPN
ejpam-412	119	3	,	,	PUNCT
ejpam-412	119	4	y(x	y(x	PROPN
ejpam-412	119	5	)	)	PUNCT
ejpam-412	119	6	=	=	SYM
ejpam-412	119	7	∑∞	∑∞	NOUN
ejpam-412	119	8	k=0	k=0	PROPN
ejpam-412	119	9	h	h	NOUN
ejpam-412	119	10	1	1	NUM
ejpam-412	119	11	(	(	PUNCT
ejpam-412	119	12	2	2	NUM
ejpam-412	119	13	j+1	j+1	NUM
ejpam-412	119	14	)	)	PUNCT
ejpam-412	119	15	!	!	PUNCT
ejpam-412	120	1	γ2	γ2	NOUN
ejpam-412	120	2	j+1	j+1	PUNCT
ejpam-412	121	1	i	i	PRON
ejpam-412	121	2	y	y	PROPN
ejpam-412	121	3	(	(	PUNCT
ejpam-412	121	4	k)x	k)x	X
ejpam-412	121	5	k.	k.	PROPN
ejpam-412	121	6	(	(	PUNCT
ejpam-412	121	7	4.8	4.8	NUM
ejpam-412	121	8	)	)	PUNCT
ejpam-412	121	9	noting	note	VERB
ejpam-412	121	10	that	that	SCONJ
ejpam-412	121	11	y(2r+1)(0	y(2r+1)(0	PROPN
ejpam-412	121	12	)	)	PUNCT
ejpam-412	122	1	=	=	SYM
ejpam-412	122	2	ar	ar	NOUN
ejpam-412	122	3	,	,	PUNCT
ejpam-412	122	4	r	r	NOUN
ejpam-412	122	5	=	=	SYM
ejpam-412	122	6	0	0	NUM
ejpam-412	122	7	,	,	PUNCT
ejpam-412	122	8	1	1	NUM
ejpam-412	122	9	,	,	PUNCT
ejpam-412	122	10	2	2	NUM
ejpam-412	122	11	,	,	PUNCT
ejpam-412	122	12	.	.	PUNCT
ejpam-412	122	13	.	.	PUNCT
ejpam-412	122	14	.	.	PUNCT
ejpam-412	123	1	,	,	PUNCT
ejpam-412	123	2	(	(	PUNCT
ejpam-412	123	3	m−1	m−1	PROPN
ejpam-412	123	4	)	)	PUNCT
ejpam-412	123	5	,	,	PUNCT
ejpam-412	123	6	and	and	CCONJ
ejpam-412	123	7	y(2r)(0	y(2r)(0	NUM
ejpam-412	123	8	)	)	PUNCT
ejpam-412	124	1	=	=	SYM
ejpam-412	124	2	br	br	INTJ
ejpam-412	124	3	,	,	PUNCT
ejpam-412	124	4	r	r	NOUN
ejpam-412	124	5	=	=	SYM
ejpam-412	124	6	0	0	NUM
ejpam-412	124	7	,	,	PUNCT
ejpam-412	124	8	1	1	NUM
ejpam-412	124	9	,	,	PUNCT
ejpam-412	124	10	2	2	NUM
ejpam-412	124	11	,	,	PUNCT
ejpam-412	124	12	.	.	PUNCT
ejpam-412	124	13	.	.	PUNCT
ejpam-412	124	14	.	.	PUNCT
ejpam-412	125	1	,	,	PUNCT
ejpam-412	125	2	m	m	VERB
ejpam-412	125	3	,	,	PUNCT
ejpam-412	125	4	are	be	AUX
ejpam-412	125	5	constants	constant	NOUN
ejpam-412	125	6	that	that	PRON
ejpam-412	125	7	will	will	AUX
ejpam-412	125	8	be	be	AUX
ejpam-412	125	9	approximated	approximate	VERB
ejpam-412	125	10	at	at	ADP
ejpam-412	125	11	the	the	DET
ejpam-412	125	12	end	end	NOUN
ejpam-412	125	13	point	point	NOUN
ejpam-412	125	14	x	x	PUNCT
ejpam-412	125	15	=	=	PUNCT
ejpam-412	125	16	b.	b.	PROPN
ejpam-412	125	17	5	5	X
ejpam-412	125	18	.	.	PUNCT
ejpam-412	125	19	numerical	numerical	ADJ
ejpam-412	125	20	examples	example	NOUN
ejpam-412	125	21	in	in	ADP
ejpam-412	125	22	this	this	DET
ejpam-412	125	23	section	section	NOUN
ejpam-412	125	24	,	,	PUNCT
ejpam-412	125	25	linear	linear	ADJ
ejpam-412	125	26	and	and	CCONJ
ejpam-412	125	27	nonlinear	nonlinear	ADJ
ejpam-412	125	28	hobvps	hobvps	NOUN
ejpam-412	125	29	will	will	AUX
ejpam-412	125	30	be	be	AUX
ejpam-412	125	31	tested	test	VERB
ejpam-412	125	32	by	by	ADP
ejpam-412	125	33	using	use	VERB
ejpam-412	125	34	the	the	DET
ejpam-412	125	35	differential	differential	ADJ
ejpam-412	125	36	transformation	transformation	NOUN
ejpam-412	125	37	method	method	NOUN
ejpam-412	125	38	,	,	PUNCT
ejpam-412	125	39	(	(	PUNCT
ejpam-412	125	40	see	see	VERB
ejpam-412	125	41	[	[	X
ejpam-412	125	42	12	12	NUM
ejpam-412	125	43	]	]	PUNCT
ejpam-412	125	44	)	)	PUNCT
ejpam-412	125	45	.	.	PUNCT
ejpam-412	126	1	example	example	NOUN
ejpam-412	127	1	5.1	5.1	NUM
ejpam-412	127	2	.	.	PUNCT
ejpam-412	128	1	we	we	PRON
ejpam-412	128	2	first	first	ADV
ejpam-412	128	3	consider	consider	VERB
ejpam-412	128	4	the	the	DET
ejpam-412	128	5	following	follow	VERB
ejpam-412	128	6	linear	linear	ADJ
ejpam-412	128	7	fifth	fifth	ADJ
ejpam-412	128	8	-	-	PUNCT
ejpam-412	128	9	order	order	NOUN
ejpam-412	128	10	bvp	bvp	NOUN
ejpam-412	128	11	,	,	PUNCT
ejpam-412	128	12	which	which	PRON
ejpam-412	128	13	is	be	AUX
ejpam-412	128	14	also	also	ADV
ejpam-412	128	15	solved	solve	VERB
ejpam-412	128	16	by	by	ADP
ejpam-412	128	17	adomian	adomian	NOUN
ejpam-412	128	18	decomposition	decomposition	NOUN
ejpam-412	128	19	method	method	NOUN
ejpam-412	128	20	(	(	PUNCT
ejpam-412	128	21	adm	adm	PROPN
ejpam-412	128	22	)	)	PUNCT
ejpam-412	128	23	in	in	ADP
ejpam-412	128	24	the	the	DET
ejpam-412	128	25	study	study	NOUN
ejpam-412	128	26	of	of	ADP
ejpam-412	128	27	[	[	X
ejpam-412	128	28	21	21	NUM
ejpam-412	128	29	]	]	PUNCT
ejpam-412	128	30	y(υ)(x	y(υ)(x	NUM
ejpam-412	128	31	)	)	PUNCT
ejpam-412	128	32	=	=	SYM
ejpam-412	128	33	y(x)−	y(x)−	PROPN
ejpam-412	128	34	15ex	15ex	NOUN
ejpam-412	128	35	−	−	ADP
ejpam-412	128	36	10xex	10xex	NOUN
ejpam-412	128	37	,	,	PUNCT
ejpam-412	128	38	0	0	PUNCT
ejpam-412	128	39	<	<	X
ejpam-412	128	40	x	x	X
ejpam-412	128	41	<	<	X
ejpam-412	128	42	1	1	NUM
ejpam-412	128	43	,	,	PUNCT
ejpam-412	128	44	(	(	PUNCT
ejpam-412	128	45	5.1	5.1	NUM
ejpam-412	128	46	)	)	PUNCT
ejpam-412	128	47	subject	subject	NOUN
ejpam-412	128	48	to	to	ADP
ejpam-412	128	49	the	the	DET
ejpam-412	128	50	boundary	boundary	ADJ
ejpam-412	128	51	conditions	condition	NOUN
ejpam-412	128	52	y(0	y(0	PROPN
ejpam-412	128	53	)	)	PUNCT
ejpam-412	128	54	=	=	SYM
ejpam-412	128	55	0	0	NUM
ejpam-412	128	56	,	,	PUNCT
ejpam-412	128	57	y	y	PROPN
ejpam-412	128	58	′(0	′(0	PROPN
ejpam-412	128	59	)	)	PUNCT
ejpam-412	129	1	=	=	SYM
ejpam-412	129	2	1	1	NUM
ejpam-412	129	3	,	,	PUNCT
ejpam-412	129	4	y	y	PROPN
ejpam-412	129	5	′′(0	′′(0	PROPN
ejpam-412	129	6	)	)	PUNCT
ejpam-412	129	7	=	=	SYM
ejpam-412	129	8	0	0	NUM
ejpam-412	129	9	,	,	PUNCT
ejpam-412	129	10	y(1	y(1	PROPN
ejpam-412	129	11	)	)	PUNCT
ejpam-412	129	12	=	=	SYM
ejpam-412	129	13	0	0	NUM
ejpam-412	129	14	,	,	PUNCT
ejpam-412	129	15	y	y	PROPN
ejpam-412	129	16	′(1	′(1	PROPN
ejpam-412	129	17	)	)	PUNCT
ejpam-412	129	18	=	=	NOUN
ejpam-412	129	19	−e	−e	NOUN
ejpam-412	129	20	.	.	PUNCT
ejpam-412	130	1	(	(	PUNCT
ejpam-412	130	2	5.2	5.2	X
ejpam-412	130	3	)	)	PUNCT
ejpam-412	130	4	applying	apply	VERB
ejpam-412	130	5	the	the	DET
ejpam-412	130	6	operations	operation	NOUN
ejpam-412	130	7	of	of	ADP
ejpam-412	130	8	(	(	PUNCT
ejpam-412	130	9	dt	dt	NOUN
ejpam-412	130	10	)	)	PUNCT
ejpam-412	130	11	to	to	ADP
ejpam-412	130	12	eq	eq	NOUN
ejpam-412	130	13	.	.	PUNCT
ejpam-412	131	1	(	(	PUNCT
ejpam-412	131	2	5.1	5.1	NUM
ejpam-412	131	3	)	)	PUNCT
ejpam-412	131	4	,	,	PUNCT
ejpam-412	131	5	the	the	DET
ejpam-412	131	6	following	follow	VERB
ejpam-412	131	7	recurrence	recurrence	NOUN
ejpam-412	131	8	relation	relation	NOUN
ejpam-412	131	9	is	be	AUX
ejpam-412	131	10	obtained	obtain	VERB
ejpam-412	131	11	:	:	PUNCT
ejpam-412	131	12	y	y	PROPN
ejpam-412	131	13	(	(	PUNCT
ejpam-412	131	14	k+	k+	NOUN
ejpam-412	131	15	5	5	X
ejpam-412	131	16	)	)	PUNCT
ejpam-412	131	17	=	=	SYM
ejpam-412	132	1	k	k	X
ejpam-412	132	2	!	!	PUNCT
ejpam-412	132	3	h	h	PROPN
ejpam-412	133	1	y	y	PROPN
ejpam-412	133	2	(	(	PUNCT
ejpam-412	133	3	k)−	k)−	PROPN
ejpam-412	133	4	15	15	NUM
ejpam-412	133	5	k	k	NOUN
ejpam-412	133	6	!	!	PUNCT
ejpam-412	134	1	−10	−10	PROPN
ejpam-412	135	1	�	�	PROPN
ejpam-412	136	1	∑k	∑k	PROPN
ejpam-412	136	2	l=0	l=0	PROPN
ejpam-412	136	3	h	h	NOUN
ejpam-412	136	4	δ(k−l−1	δ(k−l−1	PROPN
ejpam-412	136	5	)	)	PUNCT
ejpam-412	137	1	l	l	NOUN
ejpam-412	137	2	!	!	PUNCT
ejpam-412	138	1	i	i	PRON
ejpam-412	138	2	�	�	VERB
ejpam-412	138	3	i	i	PRON
ejpam-412	138	4	(	(	PUNCT
ejpam-412	138	5	km+5	km+5	NOUN
ejpam-412	138	6	)	)	PUNCT
ejpam-412	138	7	!	!	PUNCT
ejpam-412	139	1	(	(	PUNCT
ejpam-412	139	2	5.3	5.3	NUM
ejpam-412	139	3	)	)	PUNCT
ejpam-412	139	4	by	by	ADP
ejpam-412	139	5	using	use	VERB
ejpam-412	139	6	eqs	eqs	PROPN
ejpam-412	139	7	.	.	PUNCT
ejpam-412	140	1	(	(	PUNCT
ejpam-412	140	2	2.1	2.1	NUM
ejpam-412	140	3	)	)	PUNCT
ejpam-412	140	4	and	and	CCONJ
ejpam-412	140	5	(	(	PUNCT
ejpam-412	140	6	5.2	5.2	NUM
ejpam-412	140	7	)	)	PUNCT
ejpam-412	141	1	the	the	DET
ejpam-412	141	2	following	follow	VERB
ejpam-412	141	3	transformed	transform	VERB
ejpam-412	141	4	b.c	b.c	PROPN
ejpam-412	141	5	.	.	PROPN
ejpam-412	141	6	’s	’s	X
ejpam-412	141	7	at	at	ADP
ejpam-412	141	8	x	x	X
ejpam-412	141	9	=	=	SYM
ejpam-412	141	10	0	0	NUM
ejpam-412	141	11	can	can	AUX
ejpam-412	141	12	be	be	AUX
ejpam-412	141	13	obtained	obtain	VERB
ejpam-412	141	14	:	:	PUNCT
ejpam-412	141	15	y	y	PROPN
ejpam-412	141	16	(	(	PUNCT
ejpam-412	141	17	0	0	NUM
ejpam-412	141	18	)	)	PUNCT
ejpam-412	141	19	=	=	SYM
ejpam-412	141	20	0	0	NUM
ejpam-412	141	21	,	,	PUNCT
ejpam-412	141	22	y	y	PROPN
ejpam-412	141	23	(	(	PUNCT
ejpam-412	141	24	1	1	NUM
ejpam-412	141	25	)	)	PUNCT
ejpam-412	141	26	=	=	SYM
ejpam-412	142	1	1	1	NUM
ejpam-412	142	2	,	,	PUNCT
ejpam-412	142	3	y	y	PROPN
ejpam-412	142	4	(	(	PUNCT
ejpam-412	142	5	2	2	NUM
ejpam-412	142	6	)	)	PUNCT
ejpam-412	142	7	=	=	SYM
ejpam-412	142	8	0	0	NUM
ejpam-412	142	9	,	,	PUNCT
ejpam-412	142	10	(	(	PUNCT
ejpam-412	142	11	5.4	5.4	NUM
ejpam-412	142	12	)	)	PUNCT
ejpam-412	142	13	where	where	SCONJ
ejpam-412	142	14	,	,	PUNCT
ejpam-412	142	15	according	accord	VERB
ejpam-412	142	16	to	to	ADP
ejpam-412	142	17	eq	eq	PROPN
ejpam-412	142	18	.	.	PUNCT
ejpam-412	143	1	(	(	PUNCT
ejpam-412	143	2	2.1	2.1	NUM
ejpam-412	143	3	)	)	PUNCT
ejpam-412	143	4	,	,	PUNCT
ejpam-412	143	5	a	a	DET
ejpam-412	143	6	=	=	SYM
ejpam-412	143	7	y′′′(0	y′′′(0	NOUN
ejpam-412	143	8	)	)	PUNCT
ejpam-412	143	9	3	3	NUM
ejpam-412	143	10	!	!	PUNCT
ejpam-412	144	1	=	=	SYM
ejpam-412	144	2	y	y	PROPN
ejpam-412	144	3	(	(	PUNCT
ejpam-412	144	4	3	3	NUM
ejpam-412	144	5	)	)	PUNCT
ejpam-412	144	6	and	and	CCONJ
ejpam-412	144	7	b	b	X
ejpam-412	144	8	=	=	SYM
ejpam-412	144	9	y(iv)(0	y(iv)(0	PROPN
ejpam-412	144	10	)	)	PUNCT
ejpam-412	144	11	4	4	NUM
ejpam-412	144	12	!	!	PUNCT
ejpam-412	144	13	=	=	SYM
ejpam-412	145	1	y	y	PROPN
ejpam-412	145	2	(	(	PUNCT
ejpam-412	145	3	4	4	NUM
ejpam-412	145	4	)	)	PUNCT
ejpam-412	145	5	.	.	PUNCT
ejpam-412	146	1	utilizing	utilize	VERB
ejpam-412	146	2	the	the	DET
ejpam-412	146	3	recurrence	recurrence	NOUN
ejpam-412	146	4	relation	relation	NOUN
ejpam-412	146	5	in	in	ADP
ejpam-412	146	6	eq	eq	ADP
ejpam-412	146	7	.	.	PUNCT
ejpam-412	147	1	(	(	PUNCT
ejpam-412	147	2	5.3	5.3	NUM
ejpam-412	147	3	)	)	PUNCT
ejpam-412	147	4	and	and	CCONJ
ejpam-412	147	5	the	the	DET
ejpam-412	147	6	transformed	transform	VERB
ejpam-412	147	7	b.c	b.c	PROPN
ejpam-412	147	8	.	.	PROPN
ejpam-412	147	9	’s	’s	PART
ejpam-412	147	10	in	in	ADP
ejpam-412	147	11	eq	eq	ADP
ejpam-412	147	12	.	.	PUNCT
ejpam-412	148	1	(	(	PUNCT
ejpam-412	148	2	5.4	5.4	NUM
ejpam-412	148	3	)	)	PUNCT
ejpam-412	148	4	,	,	PUNCT
ejpam-412	148	5	y	y	PROPN
ejpam-412	148	6	(	(	PUNCT
ejpam-412	148	7	k	k	NOUN
ejpam-412	148	8	)	)	PUNCT
ejpam-412	148	9	for	for	ADP
ejpam-412	148	10	k≥	k≥	PROPN
ejpam-412	148	11	5	5	NUM
ejpam-412	148	12	are	be	AUX
ejpam-412	148	13	easily	easily	ADV
ejpam-412	148	14	obtained	obtain	VERB
ejpam-412	148	15	.	.	PUNCT
ejpam-412	149	1	i.	i.	PROPN
ejpam-412	149	2	abdel	abdel	PROPN
ejpam-412	149	3	-	-	PUNCT
ejpam-412	149	4	halim	halim	PROPN
ejpam-412	149	5	and	and	CCONJ
ejpam-412	149	6	v.	v.	ADP
ejpam-412	149	7	ertürk	ertürk	PROPN
ejpam-412	149	8	/	/	SYM
ejpam-412	149	9	eur	eur	PROPN
ejpam-412	149	10	.	.	PUNCT
ejpam-412	150	1	j.	j.	PROPN
ejpam-412	150	2	pure	pure	PROPN
ejpam-412	150	3	appl	appl	PROPN
ejpam-412	150	4	.	.	PROPN
ejpam-412	150	5	math	math	PROPN
ejpam-412	150	6	,	,	PUNCT
ejpam-412	150	7	2	2	NUM
ejpam-412	150	8	(	(	PUNCT
ejpam-412	150	9	2009	2009	NUM
ejpam-412	150	10	)	)	PUNCT
ejpam-412	150	11	,	,	PUNCT
ejpam-412	150	12	(	(	PUNCT
ejpam-412	150	13	426	426	NUM
ejpam-412	150	14	-	-	NUM
ejpam-412	150	15	447	447	NUM
ejpam-412	150	16	)	)	PUNCT
ejpam-412	150	17	432	432	NUM
ejpam-412	151	1	the	the	DET
ejpam-412	151	2	constants	constant	NOUN
ejpam-412	151	3	a	a	PRON
ejpam-412	151	4	and	and	CCONJ
ejpam-412	151	5	b	b	NOUN
ejpam-412	151	6	are	be	AUX
ejpam-412	151	7	evaluated	evaluate	VERB
ejpam-412	151	8	from	from	ADP
ejpam-412	151	9	the	the	DET
ejpam-412	151	10	b.c	b.c	PROPN
ejpam-412	151	11	.	.	PROPN
ejpam-412	151	12	’s	’s	AUX
ejpam-412	151	13	given	give	VERB
ejpam-412	151	14	in	in	ADP
ejpam-412	151	15	eq	eq	ADP
ejpam-412	151	16	.	.	PUNCT
ejpam-412	152	1	(	(	PUNCT
ejpam-412	152	2	5.2	5.2	NUM
ejpam-412	152	3	)	)	PUNCT
ejpam-412	152	4	for	for	ADP
ejpam-412	152	5	x	x	X
ejpam-412	152	6	=	=	NOUN
ejpam-412	152	7	1	1	NUM
ejpam-412	152	8	,	,	PUNCT
ejpam-412	152	9	by	by	ADP
ejpam-412	152	10	taking	take	VERB
ejpam-412	152	11	n	n	X
ejpam-412	152	12	=	=	NUM
ejpam-412	152	13	13	13	NUM
ejpam-412	152	14	,	,	PUNCT
ejpam-412	152	15	to	to	PART
ejpam-412	152	16	obtain	obtain	VERB
ejpam-412	152	17	the	the	DET
ejpam-412	152	18	system	system	NOUN
ejpam-412	152	19	:	:	PUNCT
ejpam-412	152	20	148284463	148284463	NUM
ejpam-412	152	21	148262400	148262400	NUM
ejpam-412	152	22	a+	a+	PUNCT
ejpam-412	152	23	3632669041	3632669041	NUM
ejpam-412	152	24	3632428800	3632428800	NUM
ejpam-412	152	25	b	b	X
ejpam-412	152	26	=	=	SYM
ejpam-412	153	1	−	−	PROPN
ejpam-412	153	2	4541061529	4541061529	NUM
ejpam-412	153	3	5448643200	5448643200	NUM
ejpam-412	153	4	,	,	PUNCT
ejpam-412	153	5	239595841	239595841	NUM
ejpam-412	153	6	79833600	79833600	NUM
ejpam-412	153	7	a+	a+	PUNCT
ejpam-412	153	8	5148284463	5148284463	NUM
ejpam-412	153	9	37065600	37065600	NUM
ejpam-412	153	10	b	b	X
ejpam-412	153	11	=	=	NOUN
ejpam-412	153	12	−e+	−e+	NOUN
ejpam-412	153	13	15028547	15028547	NUM
ejpam-412	153	14	129729600	129729600	NUM
ejpam-412	153	15	.	.	PUNCT
ejpam-412	154	1	this	this	PRON
ejpam-412	154	2	in	in	ADP
ejpam-412	154	3	turn	turn	NOUN
ejpam-412	154	4	gives	give	VERB
ejpam-412	154	5	a	a	DET
ejpam-412	154	6	=	=	NOUN
ejpam-412	154	7	−0.3333315065	−0.3333315065	NOUN
ejpam-412	154	8	and	and	CCONJ
ejpam-412	154	9	b	b	NOUN
ejpam-412	154	10	=	=	NOUN
ejpam-412	154	11	−0.5000018268	−0.5000018268	PROPN
ejpam-412	154	12	.	.	PUNCT
ejpam-412	155	1	for	for	ADP
ejpam-412	155	2	n	n	NOUN
ejpam-412	155	3	=	=	SYM
ejpam-412	155	4	24	24	NUM
ejpam-412	155	5	,	,	PUNCT
ejpam-412	155	6	these	these	DET
ejpam-412	155	7	values	value	NOUN
ejpam-412	155	8	are	be	AUX
ejpam-412	155	9	a	a	DET
ejpam-412	155	10	=	=	X
ejpam-412	155	11	−0.333315040	−0.333315040	X
ejpam-412	155	12	and	and	CCONJ
ejpam-412	155	13	b	b	NOUN
ejpam-412	155	14	=	=	NOUN
ejpam-412	155	15	−0.5000018292	−0.5000018292	NOUN
ejpam-412	155	16	.	.	PUNCT
ejpam-412	156	1	then	then	ADV
ejpam-412	156	2	,	,	PUNCT
ejpam-412	156	3	by	by	ADP
ejpam-412	156	4	using	use	VERB
ejpam-412	156	5	the	the	DET
ejpam-412	156	6	inverse	inverse	NOUN
ejpam-412	156	7	transformation	transformation	NOUN
ejpam-412	156	8	rule	rule	NOUN
ejpam-412	156	9	in	in	ADP
ejpam-412	156	10	eq	eq	PROPN
ejpam-412	156	11	.	.	PUNCT
ejpam-412	157	1	(	(	PUNCT
ejpam-412	157	2	4.2	4.2	NUM
ejpam-412	157	3	)	)	PUNCT
ejpam-412	157	4	,	,	PUNCT
ejpam-412	157	5	we	we	PRON
ejpam-412	157	6	get	get	VERB
ejpam-412	157	7	the	the	DET
ejpam-412	157	8	following	follow	VERB
ejpam-412	157	9	series	series	NOUN
ejpam-412	157	10	solution	solution	NOUN
ejpam-412	157	11	is	be	AUX
ejpam-412	157	12	evaluated	evaluate	VERB
ejpam-412	157	13	up	up	ADP
ejpam-412	157	14	to	to	ADP
ejpam-412	157	15	n	n	NOUN
ejpam-412	157	16	=	=	NUM
ejpam-412	157	17	24	24	NUM
ejpam-412	157	18	:	:	PUNCT
ejpam-412	157	19	example	example	NOUN
ejpam-412	157	20	5.2	5.2	NUM
ejpam-412	157	21	.	.	PUNCT
ejpam-412	158	1	we	we	PRON
ejpam-412	158	2	next	next	ADV
ejpam-412	158	3	consider	consider	VERB
ejpam-412	158	4	the	the	DET
ejpam-412	158	5	following	follow	VERB
ejpam-412	158	6	non	non	ADJ
ejpam-412	158	7	-	-	ADJ
ejpam-412	158	8	linear	linear	ADJ
ejpam-412	158	9	fifth	fifth	ADJ
ejpam-412	158	10	-	-	PUNCT
ejpam-412	158	11	order	order	NOUN
ejpam-412	158	12	bvp	bvp	NOUN
ejpam-412	158	13	y(υ)(x	y(υ)(x	PROPN
ejpam-412	158	14	)	)	PUNCT
ejpam-412	158	15	=	=	NUM
ejpam-412	158	16	e−x	e−x	PROPN
ejpam-412	158	17	y2(x	y2(x	PROPN
ejpam-412	158	18	)	)	PUNCT
ejpam-412	158	19	,	,	PUNCT
ejpam-412	158	20	0	0	PUNCT
ejpam-412	158	21	<	<	X
ejpam-412	158	22	x	x	X
ejpam-412	158	23	<	<	X
ejpam-412	158	24	1	1	NUM
ejpam-412	158	25	,	,	PUNCT
ejpam-412	158	26	(	(	PUNCT
ejpam-412	158	27	5.5	5.5	NUM
ejpam-412	158	28	)	)	PUNCT
ejpam-412	158	29	subject	subject	NOUN
ejpam-412	158	30	to	to	ADP
ejpam-412	158	31	the	the	DET
ejpam-412	158	32	boundary	boundary	ADJ
ejpam-412	158	33	conditions	condition	NOUN
ejpam-412	158	34	y(0	y(0	PROPN
ejpam-412	158	35	)	)	PUNCT
ejpam-412	158	36	=	=	PUNCT
ejpam-412	159	1	0=	0=	NUM
ejpam-412	159	2	y	y	PROPN
ejpam-412	159	3	′(0	′(0	PROPN
ejpam-412	159	4	)	)	PUNCT
ejpam-412	160	1	=	=	SYM
ejpam-412	160	2	y	y	PROPN
ejpam-412	160	3	′′(0	′′(0	PROPN
ejpam-412	160	4	)	)	PUNCT
ejpam-412	160	5	=	=	SYM
ejpam-412	160	6	1	1	NUM
ejpam-412	160	7	,	,	PUNCT
ejpam-412	160	8	y(1	y(1	PROPN
ejpam-412	160	9	)	)	PUNCT
ejpam-412	160	10	=	=	SYM
ejpam-412	160	11	y	y	PROPN
ejpam-412	160	12	′(1	′(1	PROPN
ejpam-412	160	13	)	)	PUNCT
ejpam-412	160	14	=	=	SYM
ejpam-412	161	1	e.	e.	PROPN
ejpam-412	161	2	(	(	PUNCT
ejpam-412	161	3	5.6	5.6	NUM
ejpam-412	161	4	)	)	PUNCT
ejpam-412	161	5	applying	apply	VERB
ejpam-412	161	6	the	the	DET
ejpam-412	161	7	operations	operation	NOUN
ejpam-412	161	8	of	of	ADP
ejpam-412	161	9	(	(	PUNCT
ejpam-412	161	10	dt	dt	NOUN
ejpam-412	161	11	)	)	PUNCT
ejpam-412	161	12	to	to	ADP
ejpam-412	161	13	eq	eq	NOUN
ejpam-412	161	14	.	.	PUNCT
ejpam-412	161	15	(	(	PUNCT
ejpam-412	161	16	5.6	5.6	NUM
ejpam-412	161	17	)	)	PUNCT
ejpam-412	161	18	,	,	PUNCT
ejpam-412	161	19	the	the	DET
ejpam-412	161	20	following	follow	VERB
ejpam-412	161	21	recurrence	recurrence	NOUN
ejpam-412	161	22	relation	relation	NOUN
ejpam-412	161	23	is	be	AUX
ejpam-412	161	24	obtained	obtain	VERB
ejpam-412	161	25	:	:	PUNCT
ejpam-412	161	26	y	y	PROPN
ejpam-412	161	27	(	(	PUNCT
ejpam-412	161	28	k+	k+	NOUN
ejpam-412	161	29	5	5	X
ejpam-412	161	30	)	)	PUNCT
ejpam-412	161	31	=	=	SYM
ejpam-412	162	1	k	k	X
ejpam-412	162	2	!	!	PUNCT
ejpam-412	162	3	(	(	PUNCT
ejpam-412	162	4	k+5	k+5	PROPN
ejpam-412	162	5	)	)	PUNCT
ejpam-412	162	6	!	!	PUNCT
ejpam-412	163	1	∑k	∑k	PROPN
ejpam-412	163	2	l=0	l=0	PROPN
ejpam-412	163	3	∑l	∑l	PROPN
ejpam-412	163	4	s=0	s=0	X
ejpam-412	163	5	(	(	PUNCT
ejpam-412	163	6	−1)s	−1)s	X
ejpam-412	163	7	s	s	NOUN
ejpam-412	163	8	!	!	PUNCT
ejpam-412	164	1	y	y	PROPN
ejpam-412	164	2	(	(	PUNCT
ejpam-412	164	3	l	l	NOUN
ejpam-412	164	4	−	−	PROPN
ejpam-412	164	5	s)y	s)y	NOUN
ejpam-412	164	6	(	(	PUNCT
ejpam-412	164	7	k−	k−	NOUN
ejpam-412	164	8	l	l	NOUN
ejpam-412	164	9	)	)	PUNCT
ejpam-412	164	10	.	.	PUNCT
ejpam-412	165	1	(	(	PUNCT
ejpam-412	165	2	5.7	5.7	NUM
ejpam-412	165	3	)	)	PUNCT
ejpam-412	165	4	by	by	ADP
ejpam-412	165	5	using	use	VERB
ejpam-412	165	6	eqs	eqs	PROPN
ejpam-412	165	7	.	.	PUNCT
ejpam-412	166	1	(	(	PUNCT
ejpam-412	166	2	2.1	2.1	NUM
ejpam-412	166	3	)	)	PUNCT
ejpam-412	166	4	and	and	CCONJ
ejpam-412	166	5	(	(	PUNCT
ejpam-412	166	6	5.7	5.7	NUM
ejpam-412	166	7	)	)	PUNCT
ejpam-412	167	1	the	the	DET
ejpam-412	167	2	following	follow	VERB
ejpam-412	167	3	transformed	transform	VERB
ejpam-412	167	4	b.c	b.c	PROPN
ejpam-412	167	5	.	.	PROPN
ejpam-412	167	6	’s	’s	X
ejpam-412	167	7	at	at	ADP
ejpam-412	167	8	x	x	X
ejpam-412	167	9	=	=	SYM
ejpam-412	167	10	0	0	NUM
ejpam-412	167	11	can	can	AUX
ejpam-412	167	12	be	be	AUX
ejpam-412	167	13	obtained	obtain	VERB
ejpam-412	167	14	:	:	PUNCT
ejpam-412	167	15	y	y	PROPN
ejpam-412	167	16	(	(	PUNCT
ejpam-412	167	17	0	0	NUM
ejpam-412	167	18	)	)	PUNCT
ejpam-412	167	19	=	=	SYM
ejpam-412	168	1	1	1	NUM
ejpam-412	168	2	,	,	PUNCT
ejpam-412	168	3	y	y	PROPN
ejpam-412	168	4	(	(	PUNCT
ejpam-412	168	5	1	1	NUM
ejpam-412	168	6	)	)	PUNCT
ejpam-412	168	7	=	=	SYM
ejpam-412	168	8	1	1	NUM
ejpam-412	168	9	,	,	PUNCT
ejpam-412	168	10	y	y	PROPN
ejpam-412	168	11	(	(	PUNCT
ejpam-412	168	12	2	2	NUM
ejpam-412	168	13	)	)	PUNCT
ejpam-412	168	14	=	=	SYM
ejpam-412	168	15	1	1	NUM
ejpam-412	168	16	2	2	NUM
ejpam-412	168	17	,	,	PUNCT
ejpam-412	168	18	(	(	PUNCT
ejpam-412	168	19	5.8	5.8	NUM
ejpam-412	168	20	)	)	PUNCT
ejpam-412	168	21	i.	i.	PROPN
ejpam-412	168	22	abdel	abdel	PROPN
ejpam-412	168	23	-	-	PUNCT
ejpam-412	168	24	halim	halim	PROPN
ejpam-412	168	25	and	and	CCONJ
ejpam-412	168	26	v.	v.	ADP
ejpam-412	168	27	ertürk	ertürk	PROPN
ejpam-412	168	28	/	/	SYM
ejpam-412	168	29	eur	eur	PROPN
ejpam-412	168	30	.	.	PUNCT
ejpam-412	169	1	j.	j.	PROPN
ejpam-412	169	2	pure	pure	PROPN
ejpam-412	169	3	appl	appl	PROPN
ejpam-412	169	4	.	.	PROPN
ejpam-412	169	5	math	math	PROPN
ejpam-412	169	6	,	,	PUNCT
ejpam-412	169	7	2	2	NUM
ejpam-412	169	8	(	(	PUNCT
ejpam-412	169	9	2009	2009	NUM
ejpam-412	169	10	)	)	PUNCT
ejpam-412	169	11	,	,	PUNCT
ejpam-412	169	12	(	(	PUNCT
ejpam-412	169	13	426	426	NUM
ejpam-412	169	14	-	-	NUM
ejpam-412	169	15	447	447	NUM
ejpam-412	169	16	)	)	PUNCT
ejpam-412	169	17	433	433	NUM
ejpam-412	169	18	where	where	SCONJ
ejpam-412	169	19	,	,	PUNCT
ejpam-412	169	20	according	accord	VERB
ejpam-412	169	21	to	to	ADP
ejpam-412	169	22	eq	eq	PROPN
ejpam-412	169	23	.	.	PUNCT
ejpam-412	170	1	(	(	PUNCT
ejpam-412	170	2	2.1	2.1	NUM
ejpam-412	170	3	)	)	PUNCT
ejpam-412	170	4	,	,	PUNCT
ejpam-412	170	5	a1	a1	NOUN
ejpam-412	170	6	=	=	SYM
ejpam-412	170	7	y′′′(0	y′′′(0	NOUN
ejpam-412	170	8	)	)	PUNCT
ejpam-412	170	9	3	3	NUM
ejpam-412	170	10	!	!	PUNCT
ejpam-412	171	1	=	=	SYM
ejpam-412	171	2	y	y	PROPN
ejpam-412	171	3	(	(	PUNCT
ejpam-412	171	4	3	3	NUM
ejpam-412	171	5	)	)	PUNCT
ejpam-412	171	6	and	and	CCONJ
ejpam-412	171	7	a2	a2	PROPN
ejpam-412	171	8	=	=	SYM
ejpam-412	171	9	y(iv)(0	y(iv)(0	PROPN
ejpam-412	171	10	)	)	PUNCT
ejpam-412	171	11	4	4	NUM
ejpam-412	171	12	!	!	PUNCT
ejpam-412	171	13	=	=	SYM
ejpam-412	172	1	y	y	PROPN
ejpam-412	172	2	(	(	PUNCT
ejpam-412	172	3	4	4	NUM
ejpam-412	172	4	)	)	PUNCT
ejpam-412	172	5	.	.	PUNCT
ejpam-412	173	1	utilizing	utilize	VERB
ejpam-412	173	2	the	the	DET
ejpam-412	173	3	recurrence	recurrence	NOUN
ejpam-412	173	4	relation	relation	NOUN
ejpam-412	173	5	in	in	ADP
ejpam-412	173	6	eq	eq	ADP
ejpam-412	173	7	.	.	PUNCT
ejpam-412	174	1	(	(	PUNCT
ejpam-412	174	2	5.3	5.3	NUM
ejpam-412	174	3	)	)	PUNCT
ejpam-412	174	4	and	and	CCONJ
ejpam-412	174	5	the	the	DET
ejpam-412	174	6	transformed	transform	VERB
ejpam-412	174	7	b.c	b.c	PROPN
ejpam-412	174	8	.	.	PROPN
ejpam-412	174	9	’s	’s	PART
ejpam-412	174	10	in	in	ADP
ejpam-412	174	11	eq	eq	ADP
ejpam-412	174	12	.	.	PUNCT
ejpam-412	175	1	(	(	PUNCT
ejpam-412	175	2	5.4	5.4	NUM
ejpam-412	175	3	)	)	PUNCT
ejpam-412	175	4	,	,	PUNCT
ejpam-412	175	5	y	y	PROPN
ejpam-412	175	6	(	(	PUNCT
ejpam-412	175	7	k	k	NOUN
ejpam-412	175	8	)	)	PUNCT
ejpam-412	175	9	for	for	ADP
ejpam-412	175	10	k≥	k≥	PROPN
ejpam-412	175	11	5	5	NUM
ejpam-412	175	12	are	be	AUX
ejpam-412	175	13	easily	easily	ADV
ejpam-412	175	14	obtained	obtain	VERB
ejpam-412	175	15	.	.	PUNCT
ejpam-412	176	1	the	the	DET
ejpam-412	176	2	constants	constant	NOUN
ejpam-412	176	3	a1	a1	NOUN
ejpam-412	176	4	and	and	CCONJ
ejpam-412	176	5	a2	a2	PROPN
ejpam-412	176	6	are	be	AUX
ejpam-412	176	7	evaluated	evaluate	VERB
ejpam-412	176	8	from	from	ADP
ejpam-412	176	9	the	the	DET
ejpam-412	176	10	b.c	b.c	PROPN
ejpam-412	176	11	.	.	PROPN
ejpam-412	176	12	’s	’s	AUX
ejpam-412	176	13	given	give	VERB
ejpam-412	176	14	in	in	ADP
ejpam-412	176	15	eq	eq	ADP
ejpam-412	176	16	.	.	PUNCT
ejpam-412	177	1	(	(	PUNCT
ejpam-412	177	2	5.7	5.7	NUM
ejpam-412	177	3	)	)	PUNCT
ejpam-412	177	4	for	for	ADP
ejpam-412	177	5	x	x	SYM
ejpam-412	177	6	=	=	SYM
ejpam-412	177	7	1	1	NUM
ejpam-412	177	8	,	,	PUNCT
ejpam-412	177	9	by	by	ADP
ejpam-412	177	10	taking	take	VERB
ejpam-412	177	11	n	n	NOUN
ejpam-412	177	12	=	=	NUM
ejpam-412	177	13	12	12	NUM
ejpam-412	177	14	,	,	PUNCT
ejpam-412	177	15	to	to	PART
ejpam-412	177	16	obtain	obtain	VERB
ejpam-412	177	17	the	the	DET
ejpam-412	177	18	system	system	NOUN
ejpam-412	177	19	:	:	PUNCT
ejpam-412	177	20	e−	e−	PROPN
ejpam-412	177	21	80149541	80149541	NUM
ejpam-412	177	22	31933440	31933440	NUM
ejpam-412	177	23	=	=	SYM
ejpam-412	177	24	98589	98589	NUM
ejpam-412	177	25	98560	98560	NUM
ejpam-412	177	26	a1	a1	NOUN
ejpam-412	177	27	+	+	CCONJ
ejpam-412	177	28	1996097	1996097	NUM
ejpam-412	177	29	1996097	1996097	NUM
ejpam-412	177	30	a2	a2	NOUN
ejpam-412	177	31	+	+	CCONJ
ejpam-412	177	32	1	1	NUM
ejpam-412	177	33	133056	133056	NUM
ejpam-412	177	34	a2	a2	PROPN
ejpam-412	177	35	1	1	NUM
ejpam-412	177	36	+	+	CCONJ
ejpam-412	177	37	1	1	NUM
ejpam-412	177	38	47520	47520	NUM
ejpam-412	177	39	a1a2	a1a2	PROPN
ejpam-412	177	40	,	,	PUNCT
ejpam-412	177	41	e−	e−	PROPN
ejpam-412	177	42	5848303	5848303	NUM
ejpam-412	177	43	2851200	2851200	NUM
ejpam-412	178	1	=	=	SYM
ejpam-412	178	2	285343	285343	NUM
ejpam-412	178	3	95040	95040	NUM
ejpam-412	178	4	a1	a1	NOUN
ejpam-412	178	5	+	+	CCONJ
ejpam-412	178	6	665471	665471	NUM
ejpam-412	178	7	166320	166320	NUM
ejpam-412	178	8	a2	a2	PROPN
ejpam-412	178	9	+	+	CCONJ
ejpam-412	178	10	1	1	NUM
ejpam-412	178	11	13860	13860	NUM
ejpam-412	178	12	a2	a2	PROPN
ejpam-412	178	13	1	1	NUM
ejpam-412	178	14	+	+	CCONJ
ejpam-412	178	15	1	1	NUM
ejpam-412	178	16	3960	3960	NUM
ejpam-412	178	17	a1a2	a1a2	PROPN
ejpam-412	178	18	.	.	PUNCT
ejpam-412	179	1	this	this	PRON
ejpam-412	179	2	in	in	ADP
ejpam-412	179	3	turn	turn	NOUN
ejpam-412	179	4	gives	give	VERB
ejpam-412	179	5	a1	a1	NOUN
ejpam-412	179	6	=	=	PUNCT
ejpam-412	179	7	0.666611767	0.666611767	NUM
ejpam-412	179	8	and	and	CCONJ
ejpam-412	179	9	a2	a2	PROPN
ejpam-412	179	10	=	=	SYM
ejpam-412	179	11	0.0416703271	0.0416703271	NUM
ejpam-412	179	12	.	.	PUNCT
ejpam-412	180	1	for	for	ADP
ejpam-412	180	2	n	n	NOUN
ejpam-412	180	3	=	=	SYM
ejpam-412	180	4	20	20	NUM
ejpam-412	180	5	,	,	PUNCT
ejpam-412	180	6	these	these	DET
ejpam-412	180	7	values	value	NOUN
ejpam-412	180	8	are	be	AUX
ejpam-412	180	9	a1	a1	NOUN
ejpam-412	180	10	=	=	PUNCT
ejpam-412	180	11	0.1666611892	0.1666611892	NUM
ejpam-412	180	12	and	and	CCONJ
ejpam-412	180	13	a2	a2	PROPN
ejpam-412	180	14	=	=	SYM
ejpam-412	180	15	0.0416703549	0.0416703549	NUM
ejpam-412	180	16	.	.	PUNCT
ejpam-412	181	1	then	then	ADV
ejpam-412	181	2	,	,	PUNCT
ejpam-412	181	3	by	by	ADP
ejpam-412	181	4	using	use	VERB
ejpam-412	181	5	the	the	DET
ejpam-412	181	6	inverse	inverse	NOUN
ejpam-412	181	7	transformation	transformation	NOUN
ejpam-412	181	8	rule	rule	NOUN
ejpam-412	181	9	in	in	ADP
ejpam-412	181	10	eq	eq	PROPN
ejpam-412	181	11	.	.	PUNCT
ejpam-412	182	1	(	(	PUNCT
ejpam-412	182	2	4.2	4.2	NUM
ejpam-412	182	3	)	)	PUNCT
ejpam-412	182	4	,	,	PUNCT
ejpam-412	182	5	we	we	PRON
ejpam-412	182	6	get	get	VERB
ejpam-412	182	7	the	the	DET
ejpam-412	182	8	following	follow	VERB
ejpam-412	182	9	series	series	NOUN
ejpam-412	182	10	solution	solution	NOUN
ejpam-412	182	11	is	be	AUX
ejpam-412	182	12	evaluated	evaluate	VERB
ejpam-412	182	13	up	up	ADP
ejpam-412	182	14	to	to	ADP
ejpam-412	182	15	n	n	NOUN
ejpam-412	182	16	=	=	SYM
ejpam-412	182	17	20	20	NUM
ejpam-412	182	18	:	:	PUNCT
ejpam-412	182	19	numerical	numerical	ADJ
ejpam-412	182	20	results	result	NOUN
ejpam-412	182	21	for	for	ADP
ejpam-412	182	22	linear	linear	ADJ
ejpam-412	182	23	and	and	CCONJ
ejpam-412	182	24	non	non	ADJ
ejpam-412	182	25	-	-	ADJ
ejpam-412	182	26	linear	linear	ADJ
ejpam-412	182	27	of	of	ADP
ejpam-412	182	28	fifthorder	fifthorder	PROPN
ejpam-412	182	29	bvp	bvp	PROPN
ejpam-412	182	30	’s	’s	PART
ejpam-412	182	31	,	,	PUNCT
ejpam-412	182	32	the	the	DET
ejpam-412	182	33	differential	differential	ADJ
ejpam-412	182	34	transformation	transformation	NOUN
ejpam-412	182	35	method	method	NOUN
ejpam-412	182	36	(	(	PUNCT
ejpam-412	182	37	dtm	dtm	PROPN
ejpam-412	182	38	)	)	PUNCT
ejpam-412	182	39	with	with	ADP
ejpam-412	182	40	comparison	comparison	NOUN
ejpam-412	182	41	to	to	ADP
ejpam-412	182	42	the	the	DET
ejpam-412	182	43	exact	exact	ADJ
ejpam-412	182	44	solution	solution	NOUN
ejpam-412	182	45	are	be	AUX
ejpam-412	182	46	given	give	VERB
ejpam-412	182	47	in	in	ADP
ejpam-412	182	48	table	table	NOUN
ejpam-412	182	49	1	1	NUM
ejpam-412	182	50	.	.	PUNCT
ejpam-412	182	51	example	example	NOUN
ejpam-412	183	1	5.3	5.3	NUM
ejpam-412	183	2	.	.	PUNCT
ejpam-412	184	1	again	again	ADV
ejpam-412	184	2	,	,	PUNCT
ejpam-412	184	3	following	follow	VERB
ejpam-412	184	4	the	the	DET
ejpam-412	184	5	study	study	NOUN
ejpam-412	184	6	of	of	ADP
ejpam-412	184	7	[	[	X
ejpam-412	184	8	19	19	NUM
ejpam-412	184	9	]	]	PUNCT
ejpam-412	184	10	,	,	PUNCT
ejpam-412	184	11	we	we	PRON
ejpam-412	184	12	consider	consider	VERB
ejpam-412	184	13	the	the	DET
ejpam-412	184	14	following	follow	VERB
ejpam-412	184	15	linear	linear	PROPN
ejpam-412	184	16	sixthi	sixthi	PROPN
ejpam-412	184	17	.	.	PUNCT
ejpam-412	185	1	abdel	abdel	PROPN
ejpam-412	185	2	-	-	PUNCT
ejpam-412	185	3	halim	halim	PROPN
ejpam-412	185	4	and	and	CCONJ
ejpam-412	185	5	v.	v.	ADP
ejpam-412	185	6	ertürk	ertürk	PROPN
ejpam-412	185	7	/	/	SYM
ejpam-412	185	8	eur	eur	PROPN
ejpam-412	185	9	.	.	PUNCT
ejpam-412	186	1	j.	j.	PROPN
ejpam-412	186	2	pure	pure	PROPN
ejpam-412	186	3	appl	appl	PROPN
ejpam-412	186	4	.	.	PROPN
ejpam-412	186	5	math	math	PROPN
ejpam-412	186	6	,	,	PUNCT
ejpam-412	186	7	2	2	NUM
ejpam-412	186	8	(	(	PUNCT
ejpam-412	186	9	2009	2009	NUM
ejpam-412	186	10	)	)	PUNCT
ejpam-412	186	11	,	,	PUNCT
ejpam-412	186	12	(	(	PUNCT
ejpam-412	186	13	426	426	NUM
ejpam-412	186	14	-	-	NUM
ejpam-412	186	15	447	447	NUM
ejpam-412	186	16	)	)	PUNCT
ejpam-412	186	17	434	434	NUM
ejpam-412	186	18	order	order	NOUN
ejpam-412	186	19	bvp	bvp	NOUN
ejpam-412	186	20	,	,	PUNCT
ejpam-412	186	21	which	which	PRON
ejpam-412	186	22	is	be	AUX
ejpam-412	186	23	also	also	ADV
ejpam-412	186	24	solved	solve	VERB
ejpam-412	186	25	by	by	ADP
ejpam-412	186	26	adomian	adomian	NOUN
ejpam-412	186	27	decomposition	decomposition	NOUN
ejpam-412	186	28	method	method	NOUN
ejpam-412	186	29	(	(	PUNCT
ejpam-412	186	30	adm	adm	PROPN
ejpam-412	186	31	)	)	PUNCT
ejpam-412	186	32	y(vi)(x	y(vi)(x	PROPN
ejpam-412	186	33	)	)	PUNCT
ejpam-412	187	1	=	=	SYM
ejpam-412	187	2	y(x)−	y(x)−	PROPN
ejpam-412	187	3	6ex	6ex	NOUN
ejpam-412	187	4	,	,	PUNCT
ejpam-412	187	5	0	0	PUNCT
ejpam-412	187	6	<	<	X
ejpam-412	187	7	x	x	X
ejpam-412	187	8	<	<	X
ejpam-412	187	9	1	1	NUM
ejpam-412	187	10	,	,	PUNCT
ejpam-412	187	11	(	(	PUNCT
ejpam-412	187	12	5.9	5.9	NUM
ejpam-412	187	13	)	)	PUNCT
ejpam-412	187	14	subject	subject	NOUN
ejpam-412	187	15	to	to	ADP
ejpam-412	187	16	the	the	DET
ejpam-412	187	17	boundary	boundary	ADJ
ejpam-412	187	18	conditions	condition	NOUN
ejpam-412	187	19	y(0	y(0	PROPN
ejpam-412	187	20	)	)	PUNCT
ejpam-412	187	21	=	=	SYM
ejpam-412	187	22	1	1	NUM
ejpam-412	187	23	,	,	PUNCT
ejpam-412	187	24	y	y	PROPN
ejpam-412	187	25	′′(0	′′(0	PROPN
ejpam-412	187	26	)	)	PUNCT
ejpam-412	187	27	=	=	SYM
ejpam-412	187	28	−1	−1	NOUN
ejpam-412	187	29	,	,	PUNCT
ejpam-412	187	30	y(iv)(0	y(iv)(0	PROPN
ejpam-412	187	31	)	)	PUNCT
ejpam-412	188	1	=	=	NOUN
ejpam-412	188	2	−3	−3	PROPN
ejpam-412	188	3	,	,	PUNCT
ejpam-412	188	4	y(1	y(1	PROPN
ejpam-412	188	5	)	)	PUNCT
ejpam-412	188	6	=	=	SYM
ejpam-412	188	7	0	0	NUM
ejpam-412	188	8	,	,	PUNCT
ejpam-412	188	9	y	y	PROPN
ejpam-412	188	10	′′	′′	PROPN
ejpam-412	188	11	(	(	PUNCT
ejpam-412	188	12	1	1	X
ejpam-412	188	13	)	)	PUNCT
ejpam-412	188	14	=	=	NOUN
ejpam-412	188	15	−2e	−2e	PROPN
ejpam-412	188	16	,	,	PUNCT
ejpam-412	188	17	y	y	PROPN
ejpam-412	188	18	(	(	PUNCT
ejpam-412	188	19	iv	iv	PROPN
ejpam-412	188	20	)	)	PUNCT
ejpam-412	188	21	(	(	PUNCT
ejpam-412	188	22	1	1	X
ejpam-412	188	23	)	)	PUNCT
ejpam-412	188	24	=	=	SYM
ejpam-412	188	25	−4e	−4e	PROPN
ejpam-412	188	26	.	.	PUNCT
ejpam-412	188	27	(	(	PUNCT
ejpam-412	188	28	5.10	5.10	NUM
ejpam-412	188	29	)	)	PUNCT
ejpam-412	188	30	applying	apply	VERB
ejpam-412	188	31	the	the	DET
ejpam-412	188	32	operations	operation	NOUN
ejpam-412	188	33	of	of	ADP
ejpam-412	188	34	dt	dt	NOUN
ejpam-412	188	35	to	to	ADP
ejpam-412	188	36	eq	eq	PROPN
ejpam-412	188	37	.	.	PUNCT
ejpam-412	188	38	(	(	PUNCT
ejpam-412	188	39	5.11	5.11	NUM
ejpam-412	188	40	)	)	PUNCT
ejpam-412	188	41	,	,	PUNCT
ejpam-412	188	42	the	the	DET
ejpam-412	188	43	following	follow	VERB
ejpam-412	188	44	recurrence	recurrence	NOUN
ejpam-412	188	45	relation	relation	NOUN
ejpam-412	188	46	is	be	AUX
ejpam-412	188	47	obtained	obtain	VERB
ejpam-412	188	48	:	:	PUNCT
ejpam-412	188	49	y	y	PROPN
ejpam-412	188	50	(	(	PUNCT
ejpam-412	188	51	k+	k+	NOUN
ejpam-412	188	52	6	6	NUM
ejpam-412	188	53	)	)	PUNCT
ejpam-412	188	54	=	=	NOUN
ejpam-412	188	55	k![y	k![y	NOUN
ejpam-412	188	56	(	(	PUNCT
ejpam-412	188	57	k)−	k)−	PROPN
ejpam-412	188	58	6	6	NUM
ejpam-412	188	59	k	k	NOUN
ejpam-412	188	60	!	!	PUNCT
ejpam-412	188	61	]	]	PUNCT
ejpam-412	188	62	(	(	PUNCT
ejpam-412	188	63	k+6	k+6	NUM
ejpam-412	188	64	)	)	PUNCT
ejpam-412	188	65	!	!	PUNCT
ejpam-412	188	66	.	.	PUNCT
ejpam-412	189	1	(	(	PUNCT
ejpam-412	189	2	5.11	5.11	NUM
ejpam-412	189	3	)	)	PUNCT
ejpam-412	189	4	by	by	ADP
ejpam-412	189	5	using	use	VERB
ejpam-412	189	6	eqs	eqs	PROPN
ejpam-412	189	7	.	.	PUNCT
ejpam-412	190	1	(	(	PUNCT
ejpam-412	190	2	2.1	2.1	NUM
ejpam-412	190	3	)	)	PUNCT
ejpam-412	190	4	and	and	CCONJ
ejpam-412	190	5	(	(	PUNCT
ejpam-412	190	6	5.12	5.12	NUM
ejpam-412	190	7	)	)	PUNCT
ejpam-412	191	1	the	the	DET
ejpam-412	191	2	following	follow	VERB
ejpam-412	191	3	transformed	transform	VERB
ejpam-412	191	4	b.c	b.c	PROPN
ejpam-412	191	5	.	.	PROPN
ejpam-412	191	6	’s	’s	X
ejpam-412	191	7	at	at	ADP
ejpam-412	191	8	x	x	X
ejpam-412	191	9	=	=	SYM
ejpam-412	191	10	0	0	NUM
ejpam-412	191	11	can	can	AUX
ejpam-412	191	12	be	be	AUX
ejpam-412	191	13	obtained	obtain	VERB
ejpam-412	191	14	:	:	PUNCT
ejpam-412	191	15	y	y	PROPN
ejpam-412	191	16	(	(	PUNCT
ejpam-412	191	17	0	0	NUM
ejpam-412	191	18	)	)	PUNCT
ejpam-412	191	19	=	=	SYM
ejpam-412	192	1	1	1	NUM
ejpam-412	192	2	,	,	PUNCT
ejpam-412	192	3	y	y	PROPN
ejpam-412	192	4	(	(	PUNCT
ejpam-412	192	5	2	2	NUM
ejpam-412	192	6	)	)	PUNCT
ejpam-412	192	7	=	=	NOUN
ejpam-412	192	8	−1	−1	NOUN
ejpam-412	192	9	2	2	NUM
ejpam-412	192	10	,	,	PUNCT
ejpam-412	192	11	y	y	PROPN
ejpam-412	192	12	(	(	PUNCT
ejpam-412	192	13	4	4	NUM
ejpam-412	192	14	)	)	PUNCT
ejpam-412	192	15	=	=	SYM
ejpam-412	192	16	−1	−1	NOUN
ejpam-412	192	17	8	8	NUM
ejpam-412	192	18	,	,	PUNCT
ejpam-412	192	19	(	(	PUNCT
ejpam-412	192	20	5.12	5.12	NUM
ejpam-412	192	21	)	)	PUNCT
ejpam-412	192	22	where	where	SCONJ
ejpam-412	192	23	,	,	PUNCT
ejpam-412	192	24	according	accord	VERB
ejpam-412	192	25	to	to	ADP
ejpam-412	192	26	eq	eq	PROPN
ejpam-412	192	27	.	.	PUNCT
ejpam-412	193	1	(	(	PUNCT
ejpam-412	193	2	2.1	2.1	NUM
ejpam-412	193	3	)	)	PUNCT
ejpam-412	193	4	,	,	PUNCT
ejpam-412	193	5	a	a	PRON
ejpam-412	193	6	=	=	X
ejpam-412	193	7	y	y	PROPN
ejpam-412	193	8	(	(	PUNCT
ejpam-412	193	9	1	1	NUM
ejpam-412	193	10	)	)	PUNCT
ejpam-412	193	11	,	,	PUNCT
ejpam-412	193	12	b	b	X
ejpam-412	193	13	=	=	SYM
ejpam-412	193	14	y′′′(0	y′′′(0	NOUN
ejpam-412	193	15	)	)	PUNCT
ejpam-412	193	16	3	3	NUM
ejpam-412	193	17	!	!	PUNCT
ejpam-412	194	1	=	=	SYM
ejpam-412	194	2	y	y	PROPN
ejpam-412	194	3	(	(	PUNCT
ejpam-412	194	4	3	3	NUM
ejpam-412	194	5	)	)	PUNCT
ejpam-412	194	6	and	and	CCONJ
ejpam-412	194	7	c	c	X
ejpam-412	194	8	=	=	SYM
ejpam-412	194	9	y(v)(0	y(v)(0	PROPN
ejpam-412	194	10	)	)	PUNCT
ejpam-412	194	11	5	5	NUM
ejpam-412	194	12	!	!	PUNCT
ejpam-412	194	13	=	=	SYM
ejpam-412	195	1	y	y	PROPN
ejpam-412	195	2	(	(	PUNCT
ejpam-412	195	3	5	5	NUM
ejpam-412	195	4	)	)	PUNCT
ejpam-412	195	5	.	.	PUNCT
ejpam-412	196	1	utilizing	utilize	VERB
ejpam-412	196	2	the	the	DET
ejpam-412	196	3	recurrence	recurrence	NOUN
ejpam-412	196	4	relation	relation	NOUN
ejpam-412	196	5	in	in	ADP
ejpam-412	196	6	eq	eq	ADP
ejpam-412	196	7	.	.	PUNCT
ejpam-412	197	1	(	(	PUNCT
ejpam-412	197	2	5.13	5.13	NUM
ejpam-412	197	3	)	)	PUNCT
ejpam-412	197	4	and	and	CCONJ
ejpam-412	197	5	the	the	DET
ejpam-412	197	6	transformed	transform	VERB
ejpam-412	197	7	b.c	b.c	PROPN
ejpam-412	197	8	.	.	PROPN
ejpam-412	197	9	’s	’s	PART
ejpam-412	197	10	in	in	ADP
ejpam-412	197	11	eq	eq	ADP
ejpam-412	197	12	.	.	PUNCT
ejpam-412	198	1	(	(	PUNCT
ejpam-412	198	2	5.14	5.14	NUM
ejpam-412	198	3	)	)	PUNCT
ejpam-412	198	4	,	,	PUNCT
ejpam-412	198	5	y	y	PROPN
ejpam-412	198	6	(	(	PUNCT
ejpam-412	198	7	k	k	NOUN
ejpam-412	198	8	)	)	PUNCT
ejpam-412	198	9	for	for	ADP
ejpam-412	198	10	k	k	PROPN
ejpam-412	198	11	≥	≥	NUM
ejpam-412	198	12	6	6	NUM
ejpam-412	198	13	are	be	AUX
ejpam-412	198	14	easily	easily	ADV
ejpam-412	198	15	obtained	obtain	VERB
ejpam-412	198	16	.	.	PUNCT
ejpam-412	199	1	the	the	DET
ejpam-412	199	2	constants	constant	NOUN
ejpam-412	199	3	a	a	DET
ejpam-412	199	4	,	,	PUNCT
ejpam-412	199	5	b	b	NOUN
ejpam-412	199	6	and	and	CCONJ
ejpam-412	199	7	c	c	PROPN
ejpam-412	199	8	are	be	AUX
ejpam-412	199	9	evaluated	evaluate	VERB
ejpam-412	199	10	from	from	ADP
ejpam-412	199	11	the	the	DET
ejpam-412	199	12	b.c	b.c	PROPN
ejpam-412	199	13	.	.	PROPN
ejpam-412	199	14	’s	’s	AUX
ejpam-412	199	15	given	give	VERB
ejpam-412	199	16	in	in	ADP
ejpam-412	199	17	eq	eq	ADP
ejpam-412	199	18	.	.	PUNCT
ejpam-412	200	1	(	(	PUNCT
ejpam-412	200	2	5.12	5.12	NUM
ejpam-412	200	3	)	)	PUNCT
ejpam-412	200	4	for	for	ADP
ejpam-412	200	5	x	x	SYM
ejpam-412	200	6	=	=	SYM
ejpam-412	200	7	1	1	NUM
ejpam-412	200	8	,	,	PUNCT
ejpam-412	200	9	by	by	ADP
ejpam-412	200	10	taking	take	VERB
ejpam-412	200	11	n	n	X
ejpam-412	200	12	=	=	NUM
ejpam-412	200	13	13	13	NUM
ejpam-412	200	14	,	,	PUNCT
ejpam-412	200	15	to	to	PART
ejpam-412	200	16	obtain	obtain	VERB
ejpam-412	200	17	the	the	DET
ejpam-412	200	18	system	system	NOUN
ejpam-412	200	19	:	:	PUNCT
ejpam-412	200	20	889750903	889750903	NUM
ejpam-412	200	21	889574400	889574400	NUM
ejpam-412	200	22	a+	a+	PUNCT
ejpam-412	200	23	60481	60481	NUM
ejpam-412	200	24	60480	60480	NUM
ejpam-412	200	25	b+	b+	ADP
ejpam-412	200	26	332641	332641	NUM
ejpam-412	200	27	332640	332640	NUM
ejpam-412	200	28	c	c	X
ejpam-412	200	29	=	=	SYM
ejpam-412	200	30	−	−	PROPN
ejpam-412	200	31	456655181	456655181	NUM
ejpam-412	200	32	1245404160	1245404160	NUM
ejpam-412	200	33	,	,	PUNCT
ejpam-412	200	34	332641	332641	NUM
ejpam-412	200	35	39916800	39916800	NUM
ejpam-412	200	36	a+	a+	PUNCT
ejpam-412	200	37	5041	5041	NUM
ejpam-412	200	38	840	840	NUM
ejpam-412	200	39	b+	b+	ADP
ejpam-412	200	40	60481	60481	NUM
ejpam-412	200	41	3024	3024	NUM
ejpam-412	200	42	c	c	X
ejpam-412	200	43	=	=	SYM
ejpam-412	200	44	−2e+	−2e+	PROPN
ejpam-412	200	45	110549143	110549143	NUM
ejpam-412	200	46	39916800	39916800	NUM
ejpam-412	200	47	,	,	PUNCT
ejpam-412	200	48	60481	60481	NUM
ejpam-412	200	49	362880	362880	NUM
ejpam-412	200	50	a+	a+	PUNCT
ejpam-412	200	51	1	1	NUM
ejpam-412	200	52	20	20	NUM
ejpam-412	200	53	b+	b+	ADP
ejpam-412	200	54	5041	5041	NUM
ejpam-412	200	55	42	42	NUM
ejpam-412	200	56	c	c	NOUN
ejpam-412	200	57	=	=	NOUN
ejpam-412	200	58	−4e+	−4e+	PROPN
ejpam-412	200	59	829261	829261	NUM
ejpam-412	200	60	120960	120960	NUM
ejpam-412	200	61	.	.	PUNCT
ejpam-412	201	1	this	this	PRON
ejpam-412	201	2	in	in	ADP
ejpam-412	201	3	turn	turn	NOUN
ejpam-412	201	4	gives	give	VERB
ejpam-412	201	5	a	a	DET
ejpam-412	201	6	=	=	PUNCT
ejpam-412	201	7	−0.5388992288e−6	−0.5388992288e−6	PROPN
ejpam-412	201	8	,	,	PUNCT
ejpam-412	201	9	b	b	X
ejpam-412	202	1	=	=	NOUN
ejpam-412	202	2	−0.3333328229	−0.3333328229	X
ejpam-412	202	3	and	and	CCONJ
ejpam-412	202	4	c	c	NOUN
ejpam-412	202	5	=	=	SYM
ejpam-412	202	6	−0.03333330492	−0.03333330492	PROPN
ejpam-412	202	7	.	.	PUNCT
ejpam-412	203	1	for	for	ADP
ejpam-412	203	2	n	n	NOUN
ejpam-412	203	3	=	=	SYM
ejpam-412	203	4	23	23	NUM
ejpam-412	203	5	,	,	PUNCT
ejpam-412	203	6	these	these	DET
ejpam-412	203	7	values	value	NOUN
ejpam-412	203	8	are	be	AUX
ejpam-412	203	9	a	a	DET
ejpam-412	203	10	=	=	NOUN
ejpam-412	203	11	−0.4667205875e−6	−0.4667205875e−6	NOUN
ejpam-412	203	12	,	,	PUNCT
ejpam-412	203	13	b	b	NOUN
ejpam-412	203	14	=	=	SYM
ejpam-412	203	15	−0.3333329279	−0.3333329279	NOUN
ejpam-412	203	16	and	and	CCONJ
ejpam-412	203	17	c	c	NOUN
ejpam-412	203	18	=	=	SYM
ejpam-412	203	19	−0.03333327191	−0.03333327191	PROPN
ejpam-412	203	20	.	.	PUNCT
ejpam-412	204	1	then	then	ADV
ejpam-412	204	2	,	,	PUNCT
ejpam-412	204	3	by	by	ADP
ejpam-412	204	4	using	use	VERB
ejpam-412	204	5	the	the	DET
ejpam-412	204	6	inverse	inverse	NOUN
ejpam-412	204	7	transformation	transformation	NOUN
ejpam-412	204	8	rule	rule	NOUN
ejpam-412	204	9	in	in	ADP
ejpam-412	204	10	eq	eq	PROPN
ejpam-412	204	11	.	.	PUNCT
ejpam-412	205	1	(	(	PUNCT
ejpam-412	205	2	4.2	4.2	NUM
ejpam-412	205	3	)	)	PUNCT
ejpam-412	205	4	,	,	PUNCT
ejpam-412	205	5	we	we	PRON
ejpam-412	205	6	get	get	VERB
ejpam-412	205	7	the	the	DET
ejpam-412	205	8	following	follow	VERB
ejpam-412	205	9	series	series	NOUN
ejpam-412	205	10	solution	solution	NOUN
ejpam-412	205	11	is	be	AUX
ejpam-412	205	12	evaluated	evaluate	VERB
ejpam-412	205	13	up	up	ADP
ejpam-412	205	14	to	to	ADP
ejpam-412	205	15	n	n	NOUN
ejpam-412	205	16	=	=	SYM
ejpam-412	205	17	23	23	NUM
ejpam-412	205	18	:	:	PUNCT
ejpam-412	205	19	y(x	y(x	X
ejpam-412	205	20	)	)	PUNCT
ejpam-412	205	21	=	=	SYM
ejpam-412	205	22	1−	1−	NUM
ejpam-412	205	23	0.4667205875e−6	0.4667205875e−6	NOUN
ejpam-412	205	24	−	−	PROPN
ejpam-412	205	25	6x	6x	NOUN
ejpam-412	205	26	−	−	PROPN
ejpam-412	205	27	0.5x2−	0.5x2−	NOUN
ejpam-412	205	28	0.3333329279x3	0.3333329279x3	X
ejpam-412	205	29	−	−	NOUN
ejpam-412	205	30	0.125x4	0.125x4	NUM
ejpam-412	205	31	i.	i.	PROPN
ejpam-412	205	32	abdel	abdel	PROPN
ejpam-412	205	33	-	-	PUNCT
ejpam-412	205	34	halim	halim	PROPN
ejpam-412	205	35	and	and	CCONJ
ejpam-412	205	36	v.	v.	ADP
ejpam-412	205	37	ertürk	ertürk	PROPN
ejpam-412	205	38	/	/	SYM
ejpam-412	205	39	eur	eur	PROPN
ejpam-412	205	40	.	.	PUNCT
ejpam-412	206	1	j.	j.	PROPN
ejpam-412	206	2	pure	pure	PROPN
ejpam-412	206	3	appl	appl	PROPN
ejpam-412	206	4	.	.	PROPN
ejpam-412	206	5	math	math	PROPN
ejpam-412	206	6	,	,	PUNCT
ejpam-412	206	7	2	2	NUM
ejpam-412	206	8	(	(	PUNCT
ejpam-412	206	9	2009	2009	NUM
ejpam-412	206	10	)	)	PUNCT
ejpam-412	206	11	,	,	PUNCT
ejpam-412	206	12	(	(	PUNCT
ejpam-412	206	13	426	426	NUM
ejpam-412	206	14	-	-	NUM
ejpam-412	206	15	447	447	NUM
ejpam-412	206	16	)	)	PUNCT
ejpam-412	206	17	435	435	NUM
ejpam-412	206	18	−	−	NOUN
ejpam-412	206	19	0.03333327191x5	0.03333327191x5	NUM
ejpam-412	207	1	−	−	PROPN
ejpam-412	207	2	.6944444444e−2	.6944444444e−2	PUNCT
ejpam-412	208	1	−	−	PROPN
ejpam-412	209	1	2x6−	2x6−	NUM
ejpam-412	209	2	.1190476283e−2	.1190476283e−2	PUNCT
ejpam-412	210	1	−	−	PROPN
ejpam-412	210	2	2x7	2x7	NUM
ejpam-412	210	3	−	−	PROPN
ejpam-412	210	4	.1736111111e−3	.1736111111e−3	PROPN
ejpam-412	211	1	−	−	PROPN
ejpam-412	212	1	3x8−	3x8−	NUM
ejpam-412	212	2	.2204584867e−4	.2204584867e−4	PUNCT
ejpam-412	213	1	−	−	NOUN
ejpam-412	214	1	4x9−	4x9−	NUM
ejpam-412	214	2	.2480158730e−5	.2480158730e−5	PUNCT
ejpam-412	215	1	−	−	NOUN
ejpam-412	216	1	x10	x10	ADV
ejpam-412	216	2	−	−	PROPN
ejpam-412	216	3	.2505208992e−6	.2505208992e−6	PUNCT
ejpam-412	217	1	x11−	x11−	PUNCT
ejpam-412	217	2	.2296443269e−7	.2296443269e−7	PROPN
ejpam-412	218	1	x12	x12	NUM
ejpam-412	219	1	−	−	PROPN
ejpam-412	219	2	.1927085335e−8	.1927085335e−8	PROPN
ejpam-412	220	1	x13	x13	PROPN
ejpam-412	221	1	−	−	PROPN
ejpam-412	221	2	.1491196928e−9	.1491196928e−9	PROPN
ejpam-412	222	1	x14−	x14−	PROPN
ejpam-412	222	2	.1070602736e−10	.1070602736e−10	PUNCT
ejpam-412	223	1	x15−	x15−	PUNCT
ejpam-412	223	2	.7169215999e−12	.7169215999e−12	NUM
ejpam-412	224	1	x16	x16	NOUN
ejpam-412	224	2	−	−	PROPN
ejpam-412	224	3	.4498329534e−13	.4498329534e−13	PUNCT
ejpam-412	225	1	x17−	x17−	PROPN
ejpam-412	225	2	.2655265185e−14	.2655265185e−14	NUM
ejpam-412	226	1	x18−	x18−	PROPN
ejpam-412	226	2	.1479714382e−15	.1479714382e−15	PROPN
ejpam-412	227	1	x19	x19	NOUN
ejpam-412	227	2	−	−	PROPN
ejpam-412	227	3	.7809603484e−17	.7809603484e−17	PUNCT
ejpam-412	228	1	x20−	x20−	X
ejpam-412	228	2	.3914587736e−18	.3914587736e−18	PUNCT
ejpam-412	229	1	x21−	x21−	PROPN
ejpam-412	229	2	.1868326192e−19	.1868326192e−19	NUM
ejpam-412	230	1	x22	x22	NUM
ejpam-412	231	1	−	−	NOUN
ejpam-412	231	2	.8509971524e−21	.8509971524e−21	NOUN
ejpam-412	232	1	x23	x23	NUM
ejpam-412	232	2	.	.	PUNCT
ejpam-412	233	1	(	(	PUNCT
ejpam-412	233	2	5.13	5.13	NUM
ejpam-412	233	3	)	)	PUNCT
ejpam-412	233	4	example	example	NOUN
ejpam-412	233	5	5.4	5.4	NUM
ejpam-412	233	6	.	.	PUNCT
ejpam-412	234	1	we	we	PRON
ejpam-412	234	2	next	next	ADV
ejpam-412	234	3	consider	consider	VERB
ejpam-412	234	4	the	the	DET
ejpam-412	234	5	following	follow	VERB
ejpam-412	234	6	non	non	ADJ
ejpam-412	234	7	-	-	ADJ
ejpam-412	234	8	linear	linear	ADJ
ejpam-412	234	9	sixth	sixth	ADJ
ejpam-412	234	10	-	-	PUNCT
ejpam-412	234	11	order	order	NOUN
ejpam-412	234	12	bvp	bvp	NOUN
ejpam-412	234	13	y(υi)(x	y(υi)(x	PROPN
ejpam-412	234	14	)	)	PUNCT
ejpam-412	235	1	=	=	PUNCT
ejpam-412	235	2	ex	ex	X
ejpam-412	235	3	y2(x	y2(x	PROPN
ejpam-412	235	4	)	)	PUNCT
ejpam-412	235	5	,	,	PUNCT
ejpam-412	236	1	0	0	PUNCT
ejpam-412	236	2	<	<	X
ejpam-412	236	3	x	x	X
ejpam-412	236	4	<	<	X
ejpam-412	236	5	1	1	NUM
ejpam-412	236	6	,	,	PUNCT
ejpam-412	236	7	(	(	PUNCT
ejpam-412	236	8	5.14	5.14	NUM
ejpam-412	236	9	)	)	PUNCT
ejpam-412	236	10	subject	subject	NOUN
ejpam-412	236	11	to	to	ADP
ejpam-412	236	12	the	the	DET
ejpam-412	236	13	boundary	boundary	ADJ
ejpam-412	236	14	conditions	condition	NOUN
ejpam-412	236	15	y(0	y(0	PROPN
ejpam-412	236	16	)	)	PUNCT
ejpam-412	236	17	=	=	SYM
ejpam-412	237	1	1	1	NUM
ejpam-412	237	2	,	,	PUNCT
ejpam-412	237	3	y	y	PROPN
ejpam-412	237	4	′(0	′(0	PROPN
ejpam-412	237	5	)	)	PUNCT
ejpam-412	237	6	=	=	SYM
ejpam-412	237	7	−1	−1	NOUN
ejpam-412	237	8	,	,	PUNCT
ejpam-412	237	9	y	y	PROPN
ejpam-412	237	10	′′(0	′′(0	PROPN
ejpam-412	237	11	)	)	PUNCT
ejpam-412	237	12	=	=	SYM
ejpam-412	237	13	1	1	NUM
ejpam-412	237	14	,	,	PUNCT
ejpam-412	237	15	y(1	y(1	PROPN
ejpam-412	237	16	)	)	PUNCT
ejpam-412	237	17	=	=	SYM
ejpam-412	238	1	e−1	e−1	PROPN
ejpam-412	238	2	,	,	PUNCT
ejpam-412	238	3	y	y	PROPN
ejpam-412	238	4	′(1	′(1	PROPN
ejpam-412	238	5	)	)	PUNCT
ejpam-412	238	6	=	=	SYM
ejpam-412	238	7	−e−1	−e−1	NOUN
ejpam-412	238	8	,	,	PUNCT
ejpam-412	238	9	y	y	PROPN
ejpam-412	238	10	′′(1	′′(1	PROPN
ejpam-412	238	11	)	)	PUNCT
ejpam-412	238	12	=	=	SYM
ejpam-412	238	13	e−1	e−1	PROPN
ejpam-412	238	14	.	.	PUNCT
ejpam-412	239	1	(	(	PUNCT
ejpam-412	239	2	5.15	5.15	NUM
ejpam-412	239	3	)	)	PUNCT
ejpam-412	239	4	applying	apply	VERB
ejpam-412	239	5	the	the	DET
ejpam-412	239	6	operations	operation	NOUN
ejpam-412	239	7	of	of	ADP
ejpam-412	239	8	dt	dt	NOUN
ejpam-412	239	9	to	to	ADP
ejpam-412	239	10	eq	eq	PROPN
ejpam-412	239	11	.	.	PUNCT
ejpam-412	240	1	(	(	PUNCT
ejpam-412	240	2	5.16	5.16	NUM
ejpam-412	240	3	)	)	PUNCT
ejpam-412	240	4	,	,	PUNCT
ejpam-412	240	5	the	the	DET
ejpam-412	240	6	following	follow	VERB
ejpam-412	240	7	recurrence	recurrence	NOUN
ejpam-412	240	8	relation	relation	NOUN
ejpam-412	240	9	is	be	AUX
ejpam-412	240	10	obtained	obtain	VERB
ejpam-412	240	11	:	:	PUNCT
ejpam-412	240	12	y	y	PROPN
ejpam-412	240	13	(	(	PUNCT
ejpam-412	240	14	k+	k+	NOUN
ejpam-412	240	15	6	6	NUM
ejpam-412	240	16	)	)	PUNCT
ejpam-412	240	17	=	=	SYM
ejpam-412	241	1	k	k	X
ejpam-412	241	2	!	!	PUNCT
ejpam-412	241	3	(	(	PUNCT
ejpam-412	241	4	k+6	k+6	NUM
ejpam-412	241	5	)	)	PUNCT
ejpam-412	241	6	!	!	PUNCT
ejpam-412	242	1	∑k	∑k	PROPN
ejpam-412	242	2	l=0	l=0	PROPN
ejpam-412	242	3	∑l	∑l	PROPN
ejpam-412	242	4	s=0	s=0	PROPN
ejpam-412	242	5	1	1	NUM
ejpam-412	242	6	s	s	NOUN
ejpam-412	242	7	!	!	PUNCT
ejpam-412	243	1	y	y	PROPN
ejpam-412	243	2	(	(	PUNCT
ejpam-412	243	3	l	l	NOUN
ejpam-412	243	4	−	−	PROPN
ejpam-412	243	5	s)y	s)y	NOUN
ejpam-412	243	6	(	(	PUNCT
ejpam-412	243	7	k−	k−	NOUN
ejpam-412	243	8	l	l	NOUN
ejpam-412	243	9	)	)	PUNCT
ejpam-412	243	10	.	.	PUNCT
ejpam-412	244	1	(	(	PUNCT
ejpam-412	244	2	5.16	5.16	NUM
ejpam-412	244	3	)	)	PUNCT
ejpam-412	244	4	by	by	ADP
ejpam-412	244	5	using	use	VERB
ejpam-412	244	6	eqs	eqs	PROPN
ejpam-412	244	7	.	.	PUNCT
ejpam-412	245	1	(	(	PUNCT
ejpam-412	245	2	2.1	2.1	NUM
ejpam-412	245	3	)	)	PUNCT
ejpam-412	245	4	and	and	CCONJ
ejpam-412	245	5	(	(	PUNCT
ejpam-412	245	6	5.17	5.17	NUM
ejpam-412	245	7	)	)	PUNCT
ejpam-412	246	1	the	the	DET
ejpam-412	246	2	following	follow	VERB
ejpam-412	246	3	transformed	transform	VERB
ejpam-412	246	4	b.c	b.c	PROPN
ejpam-412	246	5	.	.	PROPN
ejpam-412	246	6	’s	’s	X
ejpam-412	246	7	at	at	ADP
ejpam-412	246	8	x	x	X
ejpam-412	246	9	=	=	SYM
ejpam-412	246	10	0	0	NUM
ejpam-412	246	11	can	can	AUX
ejpam-412	246	12	be	be	AUX
ejpam-412	246	13	obtained	obtain	VERB
ejpam-412	246	14	:	:	PUNCT
ejpam-412	246	15	y	y	PROPN
ejpam-412	246	16	(	(	PUNCT
ejpam-412	246	17	0	0	NUM
ejpam-412	246	18	)	)	PUNCT
ejpam-412	246	19	=	=	SYM
ejpam-412	246	20	1	1	NUM
ejpam-412	246	21	,	,	PUNCT
ejpam-412	246	22	y	y	PROPN
ejpam-412	246	23	(	(	PUNCT
ejpam-412	246	24	1	1	NUM
ejpam-412	246	25	)	)	PUNCT
ejpam-412	247	1	=	=	NOUN
ejpam-412	247	2	−1	−1	NOUN
ejpam-412	247	3	,	,	PUNCT
ejpam-412	247	4	y	y	PROPN
ejpam-412	247	5	(	(	PUNCT
ejpam-412	247	6	2	2	NUM
ejpam-412	247	7	)	)	PUNCT
ejpam-412	247	8	=	=	SYM
ejpam-412	247	9	1	1	NUM
ejpam-412	247	10	2	2	NUM
ejpam-412	247	11	,	,	PUNCT
ejpam-412	247	12	(	(	PUNCT
ejpam-412	247	13	5.17	5.17	NUM
ejpam-412	247	14	)	)	PUNCT
ejpam-412	247	15	where	where	SCONJ
ejpam-412	247	16	,	,	PUNCT
ejpam-412	247	17	according	accord	VERB
ejpam-412	247	18	to	to	ADP
ejpam-412	247	19	eq	eq	PROPN
ejpam-412	247	20	.	.	PUNCT
ejpam-412	247	21	(	(	PUNCT
ejpam-412	247	22	2.1	2.1	NUM
ejpam-412	247	23	)	)	PUNCT
ejpam-412	247	24	,	,	PUNCT
ejpam-412	247	25	a1	a1	NOUN
ejpam-412	247	26	=	=	SYM
ejpam-412	247	27	y′′′(0	y′′′(0	NOUN
ejpam-412	247	28	)	)	PUNCT
ejpam-412	247	29	3	3	NUM
ejpam-412	247	30	!	!	PUNCT
ejpam-412	247	31	=	=	SYM
ejpam-412	248	1	y	y	PROPN
ejpam-412	248	2	(	(	PUNCT
ejpam-412	248	3	3	3	NUM
ejpam-412	248	4	)	)	PUNCT
ejpam-412	248	5	,	,	PUNCT
ejpam-412	248	6	a2	a2	PROPN
ejpam-412	248	7	=	=	SYM
ejpam-412	248	8	y(iv)(0	y(iv)(0	PROPN
ejpam-412	248	9	)	)	PUNCT
ejpam-412	248	10	4	4	NUM
ejpam-412	248	11	!	!	PUNCT
ejpam-412	248	12	=	=	SYM
ejpam-412	249	1	y	y	PROPN
ejpam-412	249	2	(	(	PUNCT
ejpam-412	249	3	4	4	NUM
ejpam-412	249	4	)	)	PUNCT
ejpam-412	249	5	and	and	CCONJ
ejpam-412	249	6	a3	a3	NOUN
ejpam-412	249	7	=	=	SYM
ejpam-412	249	8	y(v)(0	y(v)(0	PROPN
ejpam-412	249	9	)	)	PUNCT
ejpam-412	249	10	5	5	NUM
ejpam-412	249	11	!	!	PUNCT
ejpam-412	249	12	=	=	SYM
ejpam-412	250	1	y	y	PROPN
ejpam-412	250	2	(	(	PUNCT
ejpam-412	250	3	5	5	NUM
ejpam-412	250	4	)	)	PUNCT
ejpam-412	250	5	.	.	PUNCT
ejpam-412	251	1	utilizing	utilize	VERB
ejpam-412	251	2	the	the	DET
ejpam-412	251	3	recurrence	recurrence	NOUN
ejpam-412	251	4	relation	relation	NOUN
ejpam-412	251	5	in	in	ADP
ejpam-412	251	6	eq	eq	ADP
ejpam-412	251	7	.	.	PUNCT
ejpam-412	252	1	(	(	PUNCT
ejpam-412	252	2	5.18	5.18	NUM
ejpam-412	252	3	)	)	PUNCT
ejpam-412	252	4	and	and	CCONJ
ejpam-412	252	5	the	the	DET
ejpam-412	252	6	transformed	transform	VERB
ejpam-412	252	7	b.c	b.c	PROPN
ejpam-412	252	8	.	.	PROPN
ejpam-412	252	9	’s	’s	PART
ejpam-412	252	10	in	in	ADP
ejpam-412	252	11	eq	eq	ADP
ejpam-412	252	12	.	.	PUNCT
ejpam-412	253	1	(	(	PUNCT
ejpam-412	253	2	5.19	5.19	NUM
ejpam-412	253	3	)	)	PUNCT
ejpam-412	253	4	,	,	PUNCT
ejpam-412	253	5	y	y	PROPN
ejpam-412	253	6	(	(	PUNCT
ejpam-412	253	7	k	k	NOUN
ejpam-412	253	8	)	)	PUNCT
ejpam-412	253	9	for	for	ADP
ejpam-412	253	10	k	k	PROPN
ejpam-412	253	11	≥	≥	NUM
ejpam-412	253	12	6	6	NUM
ejpam-412	253	13	are	be	AUX
ejpam-412	253	14	given	give	VERB
ejpam-412	253	15	.	.	PUNCT
ejpam-412	254	1	y	y	PROPN
ejpam-412	254	2	(	(	PUNCT
ejpam-412	254	3	6	6	NUM
ejpam-412	254	4	)	)	PUNCT
ejpam-412	254	5	=	=	SYM
ejpam-412	254	6	1	1	NUM
ejpam-412	254	7	720	720	NUM
ejpam-412	254	8	,	,	PUNCT
ejpam-412	254	9	y	y	PROPN
ejpam-412	254	10	(	(	PUNCT
ejpam-412	254	11	7	7	NUM
ejpam-412	254	12	)	)	PUNCT
ejpam-412	254	13	=	=	SYM
ejpam-412	255	1	−	−	PROPN
ejpam-412	255	2	1	1	NUM
ejpam-412	255	3	5040	5040	NUM
ejpam-412	255	4	,	,	PUNCT
ejpam-412	255	5	y	y	PROPN
ejpam-412	255	6	(	(	PUNCT
ejpam-412	255	7	8)	8)	NUM
ejpam-412	255	8	=	=	SYM
ejpam-412	255	9	1	1	NUM
ejpam-412	255	10	40320	40320	NUM
ejpam-412	255	11	,	,	PUNCT
ejpam-412	255	12	y	y	PROPN
ejpam-412	255	13	(	(	PUNCT
ejpam-412	255	14	9	9	NUM
ejpam-412	255	15	)	)	PUNCT
ejpam-412	255	16	=	=	SYM
ejpam-412	255	17	1	1	NUM
ejpam-412	255	18	30240	30240	NUM
ejpam-412	255	19	a1	a1	NOUN
ejpam-412	255	20	+	+	CCONJ
ejpam-412	255	21	1	1	NUM
ejpam-412	255	22	362880	362880	NUM
ejpam-412	255	23	,	,	PUNCT
ejpam-412	255	24	y	y	PROPN
ejpam-412	255	25	(	(	PUNCT
ejpam-412	255	26	10	10	NUM
ejpam-412	255	27	)	)	PUNCT
ejpam-412	255	28	=	=	SYM
ejpam-412	255	29	1	1	NUM
ejpam-412	255	30	75600	75600	NUM
ejpam-412	255	31	a2	a2	NOUN
ejpam-412	255	32	−	−	PROPN
ejpam-412	255	33	1	1	NUM
ejpam-412	255	34	3628800	3628800	NUM
ejpam-412	255	35	,	,	PUNCT
ejpam-412	255	36	y	y	PROPN
ejpam-412	255	37	(	(	PUNCT
ejpam-412	255	38	11	11	NUM
ejpam-412	255	39	)	)	PUNCT
ejpam-412	255	40	=	=	SYM
ejpam-412	255	41	1	1	NUM
ejpam-412	255	42	166320	166320	NUM
ejpam-412	255	43	a3	a3	NOUN
ejpam-412	255	44	+	+	CCONJ
ejpam-412	255	45	1	1	NUM
ejpam-412	255	46	39916800	39916800	NUM
ejpam-412	255	47	,	,	PUNCT
ejpam-412	255	48	i.	i.	PROPN
ejpam-412	255	49	abdel	abdel	PROPN
ejpam-412	255	50	-	-	PUNCT
ejpam-412	255	51	halim	halim	PROPN
ejpam-412	255	52	and	and	CCONJ
ejpam-412	255	53	v.	v.	ADP
ejpam-412	255	54	ertürk	ertürk	PROPN
ejpam-412	255	55	/	/	SYM
ejpam-412	255	56	eur	eur	PROPN
ejpam-412	255	57	.	.	PUNCT
ejpam-412	256	1	j.	j.	PROPN
ejpam-412	256	2	pure	pure	PROPN
ejpam-412	256	3	appl	appl	PROPN
ejpam-412	256	4	.	.	PROPN
ejpam-412	256	5	math	math	PROPN
ejpam-412	256	6	,	,	PUNCT
ejpam-412	256	7	2	2	NUM
ejpam-412	256	8	(	(	PUNCT
ejpam-412	256	9	2009	2009	NUM
ejpam-412	256	10	)	)	PUNCT
ejpam-412	256	11	,	,	PUNCT
ejpam-412	256	12	(	(	PUNCT
ejpam-412	256	13	426	426	NUM
ejpam-412	256	14	-	-	NUM
ejpam-412	256	15	447	447	NUM
ejpam-412	256	16	)	)	PUNCT
ejpam-412	256	17	436	436	NUM
ejpam-412	256	18	...	...	PUNCT
ejpam-412	256	19	and	and	CCONJ
ejpam-412	256	20	so	so	ADV
ejpam-412	256	21	on	on	ADV
ejpam-412	256	22	.	.	PUNCT
ejpam-412	257	1	the	the	DET
ejpam-412	257	2	constants	constant	NOUN
ejpam-412	257	3	a1	a1	PROPN
ejpam-412	257	4	,	,	PUNCT
ejpam-412	257	5	a2	a2	PROPN
ejpam-412	257	6	and	and	CCONJ
ejpam-412	257	7	a3	a3	NOUN
ejpam-412	257	8	are	be	AUX
ejpam-412	257	9	evaluated	evaluate	VERB
ejpam-412	257	10	from	from	ADP
ejpam-412	257	11	the	the	DET
ejpam-412	257	12	b.c	b.c	PROPN
ejpam-412	257	13	.	.	PROPN
ejpam-412	257	14	’s	’s	AUX
ejpam-412	257	15	given	give	VERB
ejpam-412	257	16	in	in	ADP
ejpam-412	257	17	eq	eq	ADP
ejpam-412	257	18	.	.	PUNCT
ejpam-412	258	1	(	(	PUNCT
ejpam-412	258	2	5.17	5.17	NUM
ejpam-412	258	3	)	)	PUNCT
ejpam-412	258	4	for	for	ADP
ejpam-412	258	5	x	x	SYM
ejpam-412	258	6	=	=	SYM
ejpam-412	258	7	1	1	NUM
ejpam-412	258	8	,	,	PUNCT
ejpam-412	258	9	by	by	ADP
ejpam-412	258	10	taking	take	VERB
ejpam-412	258	11	n	n	X
ejpam-412	258	12	=	=	NUM
ejpam-412	258	13	11	11	NUM
ejpam-412	258	14	,	,	PUNCT
ejpam-412	258	15	to	to	PART
ejpam-412	258	16	obtain	obtain	VERB
ejpam-412	258	17	the	the	DET
ejpam-412	258	18	system	system	NOUN
ejpam-412	258	19	:	:	PUNCT
ejpam-412	258	20	e−1	e−1	PROPN
ejpam-412	258	21	−	−	PROPN
ejpam-412	258	22	2000701	2000701	NUM
ejpam-412	258	23	3991680	3991680	NUM
ejpam-412	258	24	=	=	SYM
ejpam-412	258	25	30241	30241	NUM
ejpam-412	258	26	30240	30240	NUM
ejpam-412	258	27	a1	a1	NOUN
ejpam-412	258	28	+	+	CCONJ
ejpam-412	258	29	75601	75601	NUM
ejpam-412	258	30	75600	75600	NUM
ejpam-412	258	31	a2	a2	PROPN
ejpam-412	258	32	+	+	CCONJ
ejpam-412	258	33	166321	166321	NUM
ejpam-412	258	34	166320	166320	NUM
ejpam-412	258	35	a3	a3	NOUN
ejpam-412	258	36	,	,	PUNCT
ejpam-412	258	37	−e−1	−e−1	NUM
ejpam-412	258	38	−	−	NOUN
ejpam-412	258	39	321	321	NUM
ejpam-412	258	40	44800	44800	NUM
ejpam-412	258	41	=	=	SYM
ejpam-412	258	42	10081	10081	NUM
ejpam-412	258	43	3360	3360	NUM
ejpam-412	258	44	a1	a1	NOUN
ejpam-412	258	45	+	+	CCONJ
ejpam-412	258	46	30241	30241	NUM
ejpam-412	258	47	7560	7560	NUM
ejpam-412	258	48	a2	a2	NOUN
ejpam-412	258	49	+	+	CCONJ
ejpam-412	258	50	75601	75601	NUM
ejpam-412	258	51	15120	15120	NUM
ejpam-412	258	52	a3	a3	NOUN
ejpam-412	258	53	,	,	PUNCT
ejpam-412	258	54	e−1	e−1	PROPN
ejpam-412	258	55	−	−	PROPN
ejpam-412	258	56	46943	46943	NUM
ejpam-412	258	57	45630	45630	NUM
ejpam-412	259	1	=	=	SYM
ejpam-412	259	2	2521	2521	NUM
ejpam-412	259	3	420	420	NUM
ejpam-412	259	4	a1	a1	NOUN
ejpam-412	259	5	+	+	CCONJ
ejpam-412	259	6	10081	10081	NUM
ejpam-412	259	7	840	840	NUM
ejpam-412	259	8	a2	a2	PROPN
ejpam-412	259	9	+	+	CCONJ
ejpam-412	259	10	30241	30241	NUM
ejpam-412	259	11	1512	1512	NUM
ejpam-412	259	12	a3	a3	NOUN
ejpam-412	259	13	.	.	PUNCT
ejpam-412	260	1	this	this	PRON
ejpam-412	260	2	in	in	ADP
ejpam-412	260	3	turn	turn	NOUN
ejpam-412	260	4	gives	give	VERB
ejpam-412	260	5	a1	a1	NOUN
ejpam-412	260	6	=	=	SYM
ejpam-412	260	7	−.1666630261	−.1666630261	PROPN
ejpam-412	260	8	,	,	PUNCT
ejpam-412	260	9	a2	a2	PROPN
ejpam-412	260	10	=	=	SYM
ejpam-412	260	11	.04166085689	.04166085689	PROPN
ejpam-412	260	12	and	and	CCONJ
ejpam-412	260	13	a3	a3	NOUN
ejpam-412	260	14	=	=	NOUN
ejpam-412	260	15	.008330914797	.008330914797	PROPN
ejpam-412	260	16	.	.	PUNCT
ejpam-412	261	1	for	for	ADP
ejpam-412	261	2	n	n	NOUN
ejpam-412	261	3	=	=	SYM
ejpam-412	261	4	17	17	NUM
ejpam-412	261	5	,	,	PUNCT
ejpam-412	261	6	these	these	DET
ejpam-412	261	7	values	value	NOUN
ejpam-412	261	8	are	be	AUX
ejpam-412	261	9	a1	a1	NOUN
ejpam-412	261	10	=	=	PUNCT
ejpam-412	261	11	.1666633333	.1666633333	NOUN
ejpam-412	261	12	,	,	PUNCT
ejpam-412	261	13	a2	a2	PROPN
ejpam-412	261	14	=	=	SYM
ejpam-412	261	15	.04166152737	.04166152737	PROPN
ejpam-412	261	16	and	and	CCONJ
ejpam-412	261	17	a3	a3	NOUN
ejpam-412	261	18	=	=	SYM
ejpam-412	261	19	−.008331283835	−.008331283835	NOUN
ejpam-412	261	20	.	.	PUNCT
ejpam-412	262	1	then	then	ADV
ejpam-412	262	2	,	,	PUNCT
ejpam-412	262	3	by	by	ADP
ejpam-412	262	4	using	use	VERB
ejpam-412	262	5	the	the	DET
ejpam-412	262	6	inverse	inverse	NOUN
ejpam-412	262	7	transformation	transformation	NOUN
ejpam-412	262	8	rule	rule	NOUN
ejpam-412	262	9	in	in	ADP
ejpam-412	262	10	eq	eq	PROPN
ejpam-412	262	11	.	.	PUNCT
ejpam-412	263	1	(	(	PUNCT
ejpam-412	263	2	4.2	4.2	NUM
ejpam-412	263	3	)	)	PUNCT
ejpam-412	263	4	,	,	PUNCT
ejpam-412	263	5	we	we	PRON
ejpam-412	263	6	get	get	VERB
ejpam-412	263	7	the	the	DET
ejpam-412	263	8	following	follow	VERB
ejpam-412	263	9	series	series	NOUN
ejpam-412	263	10	solution	solution	NOUN
ejpam-412	263	11	is	be	AUX
ejpam-412	263	12	evaluated	evaluate	VERB
ejpam-412	263	13	up	up	ADP
ejpam-412	263	14	to	to	ADP
ejpam-412	263	15	n	n	NOUN
ejpam-412	263	16	=	=	SYM
ejpam-412	263	17	17	17	NUM
ejpam-412	263	18	:	:	PUNCT
ejpam-412	263	19	numerical	numerical	ADJ
ejpam-412	263	20	results	result	NOUN
ejpam-412	263	21	for	for	ADP
ejpam-412	263	22	linear	linear	ADJ
ejpam-412	263	23	and	and	CCONJ
ejpam-412	263	24	non	non	ADJ
ejpam-412	263	25	-	-	ADJ
ejpam-412	263	26	linear	linear	ADJ
ejpam-412	263	27	of	of	ADP
ejpam-412	263	28	sixthorder	sixthorder	PROPN
ejpam-412	263	29	bvp	bvp	PROPN
ejpam-412	263	30	,	,	PUNCT
ejpam-412	263	31	the	the	DET
ejpam-412	263	32	differential	differential	ADJ
ejpam-412	263	33	transformation	transformation	NOUN
ejpam-412	263	34	method	method	NOUN
ejpam-412	263	35	dtm	dtm	PROPN
ejpam-412	263	36	with	with	ADP
ejpam-412	263	37	comparison	comparison	NOUN
ejpam-412	263	38	to	to	ADP
ejpam-412	263	39	the	the	DET
ejpam-412	263	40	exact	exact	ADJ
ejpam-412	263	41	solution	solution	NOUN
ejpam-412	263	42	are	be	AUX
ejpam-412	263	43	given	give	VERB
ejpam-412	263	44	in	in	ADP
ejpam-412	263	45	table	table	NOUN
ejpam-412	263	46	2	2	NUM
ejpam-412	263	47	.	.	PUNCT
ejpam-412	263	48	i.	i.	PROPN
ejpam-412	263	49	abdel	abdel	PROPN
ejpam-412	263	50	-	-	PUNCT
ejpam-412	263	51	halim	halim	PROPN
ejpam-412	263	52	and	and	CCONJ
ejpam-412	263	53	v.	v.	ADP
ejpam-412	263	54	ertürk	ertürk	PROPN
ejpam-412	263	55	/	/	SYM
ejpam-412	263	56	eur	eur	PROPN
ejpam-412	263	57	.	.	PUNCT
ejpam-412	264	1	j.	j.	PROPN
ejpam-412	264	2	pure	pure	PROPN
ejpam-412	264	3	appl	appl	PROPN
ejpam-412	264	4	.	.	PROPN
ejpam-412	264	5	math	math	PROPN
ejpam-412	264	6	,	,	PUNCT
ejpam-412	264	7	2	2	NUM
ejpam-412	264	8	(	(	PUNCT
ejpam-412	264	9	2009	2009	NUM
ejpam-412	264	10	)	)	PUNCT
ejpam-412	264	11	,	,	PUNCT
ejpam-412	264	12	(	(	PUNCT
ejpam-412	264	13	426	426	NUM
ejpam-412	264	14	-	-	NUM
ejpam-412	264	15	447	447	NUM
ejpam-412	264	16	)	)	PUNCT
ejpam-412	264	17	437	437	NUM
ejpam-412	264	18	example	example	NOUN
ejpam-412	264	19	5.5	5.5	NUM
ejpam-412	264	20	.	.	PUNCT
ejpam-412	265	1	we	we	PRON
ejpam-412	265	2	consider	consider	VERB
ejpam-412	265	3	the	the	DET
ejpam-412	265	4	following	follow	VERB
ejpam-412	265	5	linear	linear	ADJ
ejpam-412	265	6	ninth	ninth	ADJ
ejpam-412	265	7	-	-	PUNCT
ejpam-412	265	8	order	order	NOUN
ejpam-412	265	9	bvp	bvp	NOUN
ejpam-412	265	10	[	[	X
ejpam-412	265	11	20	20	NUM
ejpam-412	265	12	]	]	PUNCT
ejpam-412	265	13	,	,	PUNCT
ejpam-412	265	14	y(i	y(i	PROPN
ejpam-412	265	15	x)(x	x)(x	PROPN
ejpam-412	265	16	)	)	PUNCT
ejpam-412	266	1	=	=	SYM
ejpam-412	266	2	y(x)−	y(x)−	PROPN
ejpam-412	266	3	9ex	9ex	NOUN
ejpam-412	266	4	,	,	PUNCT
ejpam-412	266	5	0	0	PUNCT
ejpam-412	266	6	<	<	X
ejpam-412	266	7	x	x	X
ejpam-412	266	8	<	<	X
ejpam-412	266	9	1	1	NUM
ejpam-412	266	10	,	,	PUNCT
ejpam-412	266	11	(	(	PUNCT
ejpam-412	266	12	5.18	5.18	NUM
ejpam-412	266	13	)	)	PUNCT
ejpam-412	266	14	subject	subject	NOUN
ejpam-412	266	15	to	to	ADP
ejpam-412	266	16	the	the	DET
ejpam-412	266	17	boundary	boundary	ADJ
ejpam-412	266	18	conditions	condition	NOUN
ejpam-412	266	19	y	y	PROPN
ejpam-412	266	20	(	(	PUNCT
ejpam-412	266	21	j)(0	j)(0	X
ejpam-412	266	22	)	)	PUNCT
ejpam-412	266	23	=	=	SYM
ejpam-412	266	24	(	(	PUNCT
ejpam-412	266	25	1−	1−	NUM
ejpam-412	266	26	j	j	NOUN
ejpam-412	266	27	)	)	PUNCT
ejpam-412	266	28	,	,	PUNCT
ejpam-412	266	29	j	j	X
ejpam-412	266	30	=	=	SYM
ejpam-412	266	31	0	0	NUM
ejpam-412	266	32	,	,	PUNCT
ejpam-412	266	33	1	1	NUM
ejpam-412	266	34	,	,	PUNCT
ejpam-412	266	35	2	2	NUM
ejpam-412	266	36	,	,	PUNCT
ejpam-412	266	37	3	3	NUM
ejpam-412	266	38	,	,	PUNCT
ejpam-412	266	39	4	4	NUM
ejpam-412	266	40	,	,	PUNCT
ejpam-412	266	41	y	y	PROPN
ejpam-412	266	42	(	(	PUNCT
ejpam-412	266	43	j)(1	j)(1	X
ejpam-412	266	44	)	)	PUNCT
ejpam-412	266	45	=	=	SYM
ejpam-412	267	1	−	−	PROPN
ejpam-412	267	2	je	je	X
ejpam-412	267	3	,	,	PUNCT
ejpam-412	267	4	j	j	PROPN
ejpam-412	267	5	=	=	SYM
ejpam-412	267	6	0	0	NUM
ejpam-412	267	7	,	,	PUNCT
ejpam-412	267	8	1	1	NUM
ejpam-412	267	9	,	,	PUNCT
ejpam-412	267	10	2	2	NUM
ejpam-412	267	11	,	,	PUNCT
ejpam-412	267	12	3	3	NUM
ejpam-412	267	13	.	.	PUNCT
ejpam-412	267	14	(	(	PUNCT
ejpam-412	267	15	5.19	5.19	NUM
ejpam-412	267	16	)	)	PUNCT
ejpam-412	267	17	applying	apply	VERB
ejpam-412	267	18	the	the	DET
ejpam-412	267	19	operations	operation	NOUN
ejpam-412	267	20	of	of	ADP
ejpam-412	267	21	dt	dt	NOUN
ejpam-412	267	22	to	to	ADP
ejpam-412	267	23	eq	eq	PROPN
ejpam-412	267	24	.	.	PUNCT
ejpam-412	267	25	(	(	PUNCT
ejpam-412	267	26	5.21	5.21	NUM
ejpam-412	267	27	)	)	PUNCT
ejpam-412	267	28	,	,	PUNCT
ejpam-412	267	29	the	the	DET
ejpam-412	267	30	following	follow	VERB
ejpam-412	267	31	recurrence	recurrence	NOUN
ejpam-412	267	32	relation	relation	NOUN
ejpam-412	267	33	is	be	AUX
ejpam-412	267	34	obtained	obtain	VERB
ejpam-412	267	35	:	:	PUNCT
ejpam-412	267	36	y	y	PROPN
ejpam-412	267	37	(	(	PUNCT
ejpam-412	267	38	k+	k+	NOUN
ejpam-412	267	39	9	9	X
ejpam-412	267	40	)	)	PUNCT
ejpam-412	267	41	=	=	NOUN
ejpam-412	267	42	k![y	k![y	NOUN
ejpam-412	267	43	(	(	PUNCT
ejpam-412	267	44	k)−	k)−	PROPN
ejpam-412	267	45	9	9	NUM
ejpam-412	267	46	k	k	NOUN
ejpam-412	267	47	!	!	PUNCT
ejpam-412	267	48	]	]	PUNCT
ejpam-412	268	1	(	(	PUNCT
ejpam-412	268	2	k+9	k+9	PROPN
ejpam-412	268	3	)	)	PUNCT
ejpam-412	268	4	!	!	PUNCT
ejpam-412	268	5	.	.	PUNCT
ejpam-412	269	1	(	(	PUNCT
ejpam-412	269	2	5.20	5.20	NUM
ejpam-412	269	3	)	)	PUNCT
ejpam-412	269	4	by	by	ADP
ejpam-412	269	5	using	use	VERB
ejpam-412	269	6	eqs	eqs	PROPN
ejpam-412	269	7	.	.	PUNCT
ejpam-412	270	1	(	(	PUNCT
ejpam-412	270	2	2.1	2.1	NUM
ejpam-412	270	3	)	)	PUNCT
ejpam-412	270	4	and	and	CCONJ
ejpam-412	270	5	(	(	PUNCT
ejpam-412	270	6	5.22	5.22	NUM
ejpam-412	270	7	)	)	PUNCT
ejpam-412	270	8	the	the	DET
ejpam-412	270	9	following	follow	VERB
ejpam-412	270	10	transformed	transform	VERB
ejpam-412	270	11	b.c	b.c	PROPN
ejpam-412	270	12	.	.	PROPN
ejpam-412	270	13	’s	’s	X
ejpam-412	270	14	at	at	ADP
ejpam-412	270	15	x	x	X
ejpam-412	270	16	=	=	SYM
ejpam-412	270	17	0	0	NUM
ejpam-412	270	18	can	can	AUX
ejpam-412	270	19	be	be	AUX
ejpam-412	270	20	obtained	obtain	VERB
ejpam-412	270	21	:	:	PUNCT
ejpam-412	270	22	y	y	PROPN
ejpam-412	270	23	(	(	PUNCT
ejpam-412	270	24	0	0	NUM
ejpam-412	270	25	)	)	PUNCT
ejpam-412	270	26	=	=	SYM
ejpam-412	270	27	1	1	NUM
ejpam-412	270	28	,	,	PUNCT
ejpam-412	270	29	y	y	PROPN
ejpam-412	270	30	(	(	PUNCT
ejpam-412	270	31	1	1	NUM
ejpam-412	270	32	)	)	PUNCT
ejpam-412	270	33	=	=	SYM
ejpam-412	270	34	0	0	NUM
ejpam-412	270	35	,	,	PUNCT
ejpam-412	270	36	y	y	PROPN
ejpam-412	270	37	(	(	PUNCT
ejpam-412	270	38	2	2	NUM
ejpam-412	270	39	)	)	PUNCT
ejpam-412	270	40	=	=	SYM
ejpam-412	271	1	−1	−1	NOUN
ejpam-412	271	2	2	2	NUM
ejpam-412	271	3	,	,	PUNCT
ejpam-412	271	4	y	y	PROPN
ejpam-412	271	5	(	(	PUNCT
ejpam-412	271	6	3	3	NUM
ejpam-412	271	7	)	)	PUNCT
ejpam-412	271	8	=	=	SYM
ejpam-412	271	9	−1	−1	NOUN
ejpam-412	271	10	3	3	NUM
ejpam-412	271	11	,	,	PUNCT
ejpam-412	271	12	y	y	PROPN
ejpam-412	271	13	(	(	PUNCT
ejpam-412	271	14	4	4	NUM
ejpam-412	271	15	)	)	PUNCT
ejpam-412	271	16	=	=	SYM
ejpam-412	271	17	−1	−1	NOUN
ejpam-412	271	18	8	8	NUM
ejpam-412	271	19	,	,	PUNCT
ejpam-412	271	20	(	(	PUNCT
ejpam-412	271	21	5.21	5.21	NUM
ejpam-412	271	22	)	)	PUNCT
ejpam-412	271	23	where	where	SCONJ
ejpam-412	271	24	,	,	PUNCT
ejpam-412	271	25	according	accord	VERB
ejpam-412	271	26	to	to	ADP
ejpam-412	271	27	eq	eq	PROPN
ejpam-412	271	28	.	.	PUNCT
ejpam-412	272	1	(	(	PUNCT
ejpam-412	272	2	2.1	2.1	NUM
ejpam-412	272	3	)	)	PUNCT
ejpam-412	272	4	,	,	PUNCT
ejpam-412	272	5	we	we	PRON
ejpam-412	272	6	have	have	VERB
ejpam-412	272	7	a	a	DET
ejpam-412	272	8	=	=	SYM
ejpam-412	272	9	y(v)(0	y(v)(0	NOUN
ejpam-412	272	10	)	)	PUNCT
ejpam-412	272	11	5	5	NUM
ejpam-412	272	12	!	!	PUNCT
ejpam-412	273	1	=	=	SYM
ejpam-412	273	2	y	y	PROPN
ejpam-412	273	3	(	(	PUNCT
ejpam-412	273	4	5	5	NUM
ejpam-412	273	5	)	)	PUNCT
ejpam-412	273	6	,	,	PUNCT
ejpam-412	273	7	b	b	X
ejpam-412	273	8	=	=	SYM
ejpam-412	273	9	y(vi)(0	y(vi)(0	PROPN
ejpam-412	273	10	)	)	PUNCT
ejpam-412	273	11	6	6	NUM
ejpam-412	273	12	!	!	PUNCT
ejpam-412	274	1	=	=	SYM
ejpam-412	274	2	y	y	PROPN
ejpam-412	274	3	(	(	PUNCT
ejpam-412	274	4	6	6	NUM
ejpam-412	274	5	)	)	PUNCT
ejpam-412	274	6	,	,	PUNCT
ejpam-412	274	7	c	c	NOUN
ejpam-412	274	8	=	=	SYM
ejpam-412	274	9	y(vii)(0	y(vii)(0	NUM
ejpam-412	274	10	)	)	PUNCT
ejpam-412	274	11	7	7	NUM
ejpam-412	274	12	!	!	PUNCT
ejpam-412	274	13	=	=	SYM
ejpam-412	275	1	y	y	PROPN
ejpam-412	275	2	(	(	PUNCT
ejpam-412	275	3	7	7	NUM
ejpam-412	275	4	)	)	PUNCT
ejpam-412	275	5	,	,	PUNCT
ejpam-412	275	6	d	d	X
ejpam-412	275	7	=	=	SYM
ejpam-412	275	8	y(viii)(0	y(viii)(0	PROPN
ejpam-412	275	9	)	)	PUNCT
ejpam-412	275	10	8	8	NUM
ejpam-412	275	11	!	!	PUNCT
ejpam-412	276	1	=	=	SYM
ejpam-412	276	2	y	y	PROPN
ejpam-412	276	3	(	(	PUNCT
ejpam-412	276	4	8)	8)	NUM
ejpam-412	276	5	.	.	PUNCT
ejpam-412	276	6	utilizing	utilize	VERB
ejpam-412	276	7	the	the	DET
ejpam-412	276	8	recurrence	recurrence	NOUN
ejpam-412	276	9	relation	relation	NOUN
ejpam-412	276	10	in	in	ADP
ejpam-412	276	11	eq	eq	ADP
ejpam-412	276	12	.	.	PUNCT
ejpam-412	276	13	(	(	PUNCT
ejpam-412	276	14	5.23	5.23	NUM
ejpam-412	276	15	)	)	PUNCT
ejpam-412	276	16	and	and	CCONJ
ejpam-412	276	17	the	the	DET
ejpam-412	276	18	transformed	transform	VERB
ejpam-412	276	19	b.c	b.c	PROPN
ejpam-412	276	20	.	.	PROPN
ejpam-412	276	21	’s	’s	PART
ejpam-412	276	22	in	in	ADP
ejpam-412	276	23	eq	eq	ADP
ejpam-412	276	24	.	.	PUNCT
ejpam-412	277	1	(	(	PUNCT
ejpam-412	277	2	5.24	5.24	NUM
ejpam-412	277	3	)	)	PUNCT
ejpam-412	277	4	,	,	PUNCT
ejpam-412	277	5	y	y	PROPN
ejpam-412	277	6	(	(	PUNCT
ejpam-412	277	7	k	k	NOUN
ejpam-412	277	8	)	)	PUNCT
ejpam-412	277	9	for	for	SCONJ
ejpam-412	277	10	k	k	PROPN
ejpam-412	277	11	≥	≥	NUM
ejpam-412	277	12	9	9	NUM
ejpam-412	277	13	are	be	AUX
ejpam-412	277	14	easily	easily	ADV
ejpam-412	277	15	obtained	obtain	VERB
ejpam-412	277	16	:	:	PUNCT
ejpam-412	277	17	y	y	PROPN
ejpam-412	277	18	(	(	PUNCT
ejpam-412	277	19	9	9	NUM
ejpam-412	277	20	)	)	PUNCT
ejpam-412	277	21	=	=	SYM
ejpam-412	278	1	−	−	PROPN
ejpam-412	278	2	1	1	NUM
ejpam-412	278	3	45360	45360	NUM
ejpam-412	278	4	,	,	PUNCT
ejpam-412	278	5	y	y	PROPN
ejpam-412	278	6	(	(	PUNCT
ejpam-412	278	7	10	10	NUM
ejpam-412	278	8	)	)	PUNCT
ejpam-412	278	9	=	=	SYM
ejpam-412	279	1	−	−	PROPN
ejpam-412	279	2	1	1	NUM
ejpam-412	279	3	403200	403200	NUM
ejpam-412	279	4	,	,	PUNCT
ejpam-412	279	5	y	y	PROPN
ejpam-412	279	6	(	(	PUNCT
ejpam-412	279	7	11	11	NUM
ejpam-412	279	8	)	)	PUNCT
ejpam-412	280	1	=	=	NOUN
ejpam-412	280	2	−	−	PROPN
ejpam-412	280	3	1	1	NUM
ejpam-412	280	4	3991680	3991680	NUM
ejpam-412	280	5	,	,	PUNCT
ejpam-412	280	6	y	y	PROPN
ejpam-412	280	7	(	(	PUNCT
ejpam-412	280	8	12	12	NUM
ejpam-412	280	9	)	)	PUNCT
ejpam-412	280	10	=	=	SYM
ejpam-412	281	1	−	−	PROPN
ejpam-412	281	2	1	1	NUM
ejpam-412	281	3	43545600	43545600	NUM
ejpam-412	281	4	,	,	PUNCT
ejpam-412	281	5	y	y	PROPN
ejpam-412	281	6	(	(	PUNCT
ejpam-412	281	7	13	13	NUM
ejpam-412	281	8	)	)	PUNCT
ejpam-412	282	1	=	=	NOUN
ejpam-412	282	2	−	−	PROPN
ejpam-412	282	3	1	1	NUM
ejpam-412	282	4	518918400	518918400	NUM
ejpam-412	282	5	,	,	PUNCT
ejpam-412	282	6	y	y	PROPN
ejpam-412	282	7	(	(	PUNCT
ejpam-412	282	8	14	14	NUM
ejpam-412	282	9	)	)	PUNCT
ejpam-412	282	10	=	=	SYM
ejpam-412	282	11	1	1	NUM
ejpam-412	282	12	726485760	726485760	NUM
ejpam-412	282	13	a−	a−	PROPN
ejpam-412	282	14	1	1	NUM
ejpam-412	282	15	726485760	726485760	NUM
ejpam-412	282	16	,	,	PUNCT
ejpam-412	282	17	i.	i.	PROPN
ejpam-412	282	18	abdel	abdel	PROPN
ejpam-412	282	19	-	-	PUNCT
ejpam-412	282	20	halim	halim	PROPN
ejpam-412	282	21	and	and	CCONJ
ejpam-412	282	22	v.	v.	ADP
ejpam-412	282	23	ertürk	ertürk	PROPN
ejpam-412	282	24	/	/	SYM
ejpam-412	282	25	eur	eur	PROPN
ejpam-412	282	26	.	.	PUNCT
ejpam-412	283	1	j.	j.	PROPN
ejpam-412	283	2	pure	pure	PROPN
ejpam-412	283	3	appl	appl	PROPN
ejpam-412	283	4	.	.	PROPN
ejpam-412	283	5	math	math	PROPN
ejpam-412	283	6	,	,	PUNCT
ejpam-412	283	7	2	2	NUM
ejpam-412	283	8	(	(	PUNCT
ejpam-412	283	9	2009	2009	NUM
ejpam-412	283	10	)	)	PUNCT
ejpam-412	283	11	,	,	PUNCT
ejpam-412	283	12	(	(	PUNCT
ejpam-412	283	13	426	426	NUM
ejpam-412	283	14	-	-	NUM
ejpam-412	283	15	447	447	NUM
ejpam-412	283	16	)	)	PUNCT
ejpam-412	283	17	438	438	NUM
ejpam-412	283	18	y	y	NOUN
ejpam-412	283	19	(	(	PUNCT
ejpam-412	283	20	15	15	NUM
ejpam-412	283	21	)	)	PUNCT
ejpam-412	283	22	=	=	SYM
ejpam-412	283	23	1	1	NUM
ejpam-412	283	24	726485760	726485760	NUM
ejpam-412	283	25	b−	b−	PROPN
ejpam-412	283	26	1	1	NUM
ejpam-412	283	27	145297152000	145297152000	NUM
ejpam-412	283	28	,	,	PUNCT
ejpam-412	283	29	y	y	PROPN
ejpam-412	283	30	(	(	PUNCT
ejpam-412	283	31	16	16	NUM
ejpam-412	283	32	)	)	PUNCT
ejpam-412	283	33	=	=	SYM
ejpam-412	284	1	1	1	NUM
ejpam-412	284	2	4151347200	4151347200	NUM
ejpam-412	284	3	c	c	NOUN
ejpam-412	284	4	−	−	PROPN
ejpam-412	284	5	1	1	NUM
ejpam-412	284	6	2324754432000	2324754432000	NUM
ejpam-412	284	7	,	,	PUNCT
ejpam-412	284	8	y	y	PROPN
ejpam-412	284	9	(	(	PUNCT
ejpam-412	284	10	17	17	NUM
ejpam-412	284	11	)	)	PUNCT
ejpam-412	284	12	=	=	SYM
ejpam-412	284	13	1	1	NUM
ejpam-412	284	14	8821612800	8821612800	NUM
ejpam-412	284	15	d	d	NOUN
ejpam-412	284	16	−	−	PROPN
ejpam-412	284	17	1	1	NUM
ejpam-412	284	18	39520825344000	39520825344000	NUM
ejpam-412	284	19	,	,	PUNCT
ejpam-412	284	20	y	y	PROPN
ejpam-412	284	21	(	(	PUNCT
ejpam-412	284	22	18	18	NUM
ejpam-412	284	23	)	)	PUNCT
ejpam-412	284	24	=	=	SYM
ejpam-412	285	1	−	−	PROPN
ejpam-412	285	2	1	1	NUM
ejpam-412	285	3	376610217984000	376610217984000	NUM
ejpam-412	285	4	,	,	PUNCT
ejpam-412	285	5	y	y	PROPN
ejpam-412	285	6	(	(	PUNCT
ejpam-412	285	7	19	19	NUM
ejpam-412	285	8	)	)	PUNCT
ejpam-412	285	9	=	=	SYM
ejpam-412	286	1	−	−	PROPN
ejpam-412	286	2	1	1	NUM
ejpam-412	286	3	6758061133824000	6758061133824000	NUM
ejpam-412	286	4	,	,	PUNCT
ejpam-412	286	5	y	y	PROPN
ejpam-412	286	6	(	(	PUNCT
ejpam-412	286	7	20	20	NUM
ejpam-412	286	8	)	)	PUNCT
ejpam-412	286	9	=	=	SYM
ejpam-412	287	1	−	−	PROPN
ejpam-412	287	2	1	1	NUM
ejpam-412	287	3	128047474114560000	128047474114560000	NUM
ejpam-412	287	4	,	,	PUNCT
ejpam-412	287	5	and	and	CCONJ
ejpam-412	287	6	so	so	ADV
ejpam-412	287	7	on	on	ADV
ejpam-412	287	8	.	.	PUNCT
ejpam-412	288	1	the	the	DET
ejpam-412	288	2	constants	constant	NOUN
ejpam-412	288	3	a	a	DET
ejpam-412	288	4	,	,	PUNCT
ejpam-412	288	5	b	b	NOUN
ejpam-412	288	6	,	,	PUNCT
ejpam-412	288	7	c	c	PROPN
ejpam-412	288	8	and	and	CCONJ
ejpam-412	288	9	d	d	PROPN
ejpam-412	288	10	are	be	AUX
ejpam-412	288	11	evaluated	evaluate	VERB
ejpam-412	288	12	from	from	ADP
ejpam-412	288	13	the	the	DET
ejpam-412	288	14	b.c	b.c	PROPN
ejpam-412	288	15	.	.	PROPN
ejpam-412	288	16	’s	’s	AUX
ejpam-412	288	17	given	give	VERB
ejpam-412	288	18	in	in	ADP
ejpam-412	288	19	eq	eq	ADP
ejpam-412	288	20	.	.	PUNCT
ejpam-412	289	1	(	(	PUNCT
ejpam-412	289	2	5.22	5.22	NUM
ejpam-412	289	3	)	)	PUNCT
ejpam-412	289	4	for	for	ADP
ejpam-412	289	5	x	x	SYM
ejpam-412	289	6	=	=	SYM
ejpam-412	289	7	1	1	NUM
ejpam-412	289	8	,	,	PUNCT
ejpam-412	289	9	by	by	ADP
ejpam-412	289	10	taking	take	VERB
ejpam-412	289	11	n	n	X
ejpam-412	289	12	=	=	NUM
ejpam-412	289	13	17	17	NUM
ejpam-412	289	14	,	,	PUNCT
ejpam-412	289	15	to	to	PART
ejpam-412	289	16	obtain	obtain	VERB
ejpam-412	289	17	the	the	DET
ejpam-412	289	18	system	system	NOUN
ejpam-412	289	19	:	:	PUNCT
ejpam-412	289	20	this	this	PRON
ejpam-412	289	21	in	in	ADP
ejpam-412	289	22	turn	turn	NOUN
ejpam-412	289	23	gives	give	VERB
ejpam-412	289	24	a	a	DET
ejpam-412	289	25	=	=	PUNCT
ejpam-412	289	26	−.3336167167e−1	−.3336167167e−1	PROPN
ejpam-412	289	27	,	,	PUNCT
ejpam-412	289	28	b	b	X
ejpam-412	289	29	=	=	SYM
ejpam-412	289	30	−.6870399019e−2	−.6870399019e−2	PROPN
ejpam-412	289	31	and	and	CCONJ
ejpam-412	289	32	c	c	NOUN
ejpam-412	289	33	=	=	SYM
ejpam-412	289	34	−.1255380280e−2	−.1255380280e−2	PROPN
ejpam-412	289	35	and	and	CCONJ
ejpam-412	289	36	d	d	X
ejpam-412	289	37	=	=	SYM
ejpam-412	289	38	−.1544141065e−3	−.1544141065e−3	PROPN
ejpam-412	289	39	.	.	PUNCT
ejpam-412	290	1	for	for	ADP
ejpam-412	290	2	n	n	NOUN
ejpam-412	290	3	=	=	SYM
ejpam-412	290	4	26	26	NUM
ejpam-412	290	5	,	,	PUNCT
ejpam-412	290	6	these	these	DET
ejpam-412	290	7	values	value	NOUN
ejpam-412	290	8	are	be	AUX
ejpam-412	290	9	a	a	DET
ejpam-412	290	10	=	=	PUNCT
ejpam-412	290	11	−.3336167167e−1	−.3336167167e−1	PROPN
ejpam-412	290	12	,	,	PUNCT
ejpam-412	290	13	b	b	X
ejpam-412	290	14	=	=	SYM
ejpam-412	290	15	−.6870399019e−2	−.6870399019e−2	PROPN
ejpam-412	290	16	and	and	CCONJ
ejpam-412	290	17	c	c	NOUN
ejpam-412	290	18	=	=	SYM
ejpam-412	290	19	−.1255380280e−2	−.1255380280e−2	PROPN
ejpam-412	290	20	and	and	CCONJ
ejpam-412	290	21	d	d	PROPN
ejpam-412	290	22	=	=	SYM
ejpam-412	290	23	−.1544141066e−3	−.1544141066e−3	PROPN
ejpam-412	290	24	.	.	PUNCT
ejpam-412	291	1	then	then	ADV
ejpam-412	291	2	,	,	PUNCT
ejpam-412	291	3	by	by	ADP
ejpam-412	291	4	using	use	VERB
ejpam-412	291	5	the	the	DET
ejpam-412	291	6	inverse	inverse	NOUN
ejpam-412	291	7	transformation	transformation	NOUN
ejpam-412	291	8	rule	rule	NOUN
ejpam-412	291	9	in	in	ADP
ejpam-412	291	10	eq	eq	PROPN
ejpam-412	291	11	.	.	PUNCT
ejpam-412	292	1	(	(	PUNCT
ejpam-412	292	2	4.2	4.2	NUM
ejpam-412	292	3	)	)	PUNCT
ejpam-412	292	4	,	,	PUNCT
ejpam-412	292	5	we	we	PRON
ejpam-412	292	6	get	get	VERB
ejpam-412	292	7	the	the	DET
ejpam-412	292	8	following	follow	VERB
ejpam-412	292	9	series	series	NOUN
ejpam-412	292	10	solution	solution	NOUN
ejpam-412	292	11	is	be	AUX
ejpam-412	292	12	evaluated	evaluate	VERB
ejpam-412	292	13	up	up	ADP
ejpam-412	292	14	to	to	ADP
ejpam-412	292	15	n	n	NOUN
ejpam-412	293	1	=	=	SYM
ejpam-412	293	2	26	26	NUM
ejpam-412	293	3	:	:	PUNCT
ejpam-412	293	4	i.	i.	PROPN
ejpam-412	293	5	abdel	abdel	PROPN
ejpam-412	293	6	-	-	PUNCT
ejpam-412	293	7	halim	halim	PROPN
ejpam-412	293	8	and	and	CCONJ
ejpam-412	293	9	v.	v.	ADP
ejpam-412	293	10	ertürk	ertürk	PROPN
ejpam-412	293	11	/	/	SYM
ejpam-412	293	12	eur	eur	PROPN
ejpam-412	293	13	.	.	PUNCT
ejpam-412	294	1	j.	j.	PROPN
ejpam-412	294	2	pure	pure	PROPN
ejpam-412	294	3	appl	appl	PROPN
ejpam-412	294	4	.	.	PROPN
ejpam-412	294	5	math	math	PROPN
ejpam-412	294	6	,	,	PUNCT
ejpam-412	294	7	2	2	NUM
ejpam-412	294	8	(	(	PUNCT
ejpam-412	294	9	2009	2009	NUM
ejpam-412	294	10	)	)	PUNCT
ejpam-412	294	11	,	,	PUNCT
ejpam-412	294	12	(	(	PUNCT
ejpam-412	294	13	426	426	NUM
ejpam-412	294	14	-	-	NUM
ejpam-412	294	15	447	447	NUM
ejpam-412	294	16	)	)	PUNCT
ejpam-412	294	17	439	439	NUM
ejpam-412	294	18	numerical	numerical	ADJ
ejpam-412	294	19	results	result	NOUN
ejpam-412	294	20	for	for	ADP
ejpam-412	294	21	linear	linear	PROPN
ejpam-412	294	22	ninthorder	ninthord	ADJ
ejpam-412	294	23	bvp	bvp	PROPN
ejpam-412	294	24	,	,	PUNCT
ejpam-412	294	25	the	the	DET
ejpam-412	294	26	differential	differential	ADJ
ejpam-412	294	27	transformation	transformation	NOUN
ejpam-412	294	28	method	method	NOUN
ejpam-412	294	29	(	(	PUNCT
ejpam-412	294	30	dtm	dtm	PROPN
ejpam-412	294	31	)	)	PUNCT
ejpam-412	294	32	with	with	ADP
ejpam-412	294	33	comparison	comparison	NOUN
ejpam-412	294	34	to	to	ADP
ejpam-412	294	35	the	the	DET
ejpam-412	294	36	exact	exact	ADJ
ejpam-412	294	37	solution	solution	NOUN
ejpam-412	294	38	are	be	AUX
ejpam-412	294	39	given	give	VERB
ejpam-412	294	40	in	in	ADP
ejpam-412	294	41	table	table	NOUN
ejpam-412	294	42	3	3	NUM
ejpam-412	294	43	.	.	PUNCT
ejpam-412	294	44	table	table	NOUN
ejpam-412	294	45	3	3	NUM
ejpam-412	294	46	:	:	PUNCT
ejpam-412	294	47	comparison	comparison	NOUN
ejpam-412	294	48	of	of	ADP
ejpam-412	294	49	numerical	numerical	ADJ
ejpam-412	294	50	result	result	NOUN
ejpam-412	294	51	of	of	ADP
ejpam-412	294	52	bvp	bvp	PROPN
ejpam-412	294	53	’s	’s	PART
ejpam-412	294	54	(	(	PUNCT
ejpam-412	294	55	5.21)-(5.22	5.21)-(5.22	NUM
ejpam-412	294	56	)	)	PUNCT
ejpam-412	294	57	see	see	VERB
ejpam-412	294	58	fig.3	fig.3	PROPN
ejpam-412	294	59	.	.	PUNCT
ejpam-412	294	60	example	example	NOUN
ejpam-412	294	61	5.6	5.6	NUM
ejpam-412	294	62	.	.	PUNCT
ejpam-412	295	1	we	we	PRON
ejpam-412	295	2	consider	consider	VERB
ejpam-412	295	3	the	the	DET
ejpam-412	295	4	following	follow	VERB
ejpam-412	295	5	non	non	ADJ
ejpam-412	295	6	-	-	ADJ
ejpam-412	295	7	linear	linear	ADJ
ejpam-412	295	8	tenth	tenth	ADJ
ejpam-412	295	9	-	-	PUNCT
ejpam-412	295	10	order	order	NOUN
ejpam-412	295	11	bvp	bvp	NOUN
ejpam-412	295	12	y(x)(x	y(x)(x	PROPN
ejpam-412	295	13	)	)	PUNCT
ejpam-412	295	14	=	=	PROPN
ejpam-412	295	15	e−x	e−x	PROPN
ejpam-412	295	16	y2(x	y2(x	PROPN
ejpam-412	295	17	)	)	PUNCT
ejpam-412	295	18	,	,	PUNCT
ejpam-412	295	19	0	0	PUNCT
ejpam-412	295	20	<	<	X
ejpam-412	295	21	x	x	X
ejpam-412	295	22	<	<	X
ejpam-412	295	23	1	1	NUM
ejpam-412	295	24	,	,	PUNCT
ejpam-412	295	25	(	(	PUNCT
ejpam-412	295	26	5.22	5.22	NUM
ejpam-412	295	27	)	)	PUNCT
ejpam-412	295	28	subject	subject	NOUN
ejpam-412	295	29	to	to	ADP
ejpam-412	295	30	the	the	DET
ejpam-412	295	31	boundary	boundary	ADJ
ejpam-412	295	32	conditions	condition	NOUN
ejpam-412	295	33	y(2	y(2	PROPN
ejpam-412	295	34	j)(0	j)(0	ADJ
ejpam-412	295	35	)	)	PUNCT
ejpam-412	295	36	=	=	SYM
ejpam-412	295	37	1	1	NUM
ejpam-412	295	38	,	,	PUNCT
ejpam-412	295	39	j	j	PROPN
ejpam-412	295	40	=	=	SYM
ejpam-412	295	41	0	0	NUM
ejpam-412	295	42	,	,	PUNCT
ejpam-412	295	43	1	1	NUM
ejpam-412	295	44	,	,	PUNCT
ejpam-412	295	45	2	2	NUM
ejpam-412	295	46	,	,	PUNCT
ejpam-412	295	47	3	3	NUM
ejpam-412	295	48	,	,	PUNCT
ejpam-412	295	49	4	4	NUM
ejpam-412	295	50	,	,	PUNCT
ejpam-412	295	51	.	.	PUNCT
ejpam-412	296	1	y(2	y(2	NOUN
ejpam-412	296	2	j)(1	j)(1	ADP
ejpam-412	296	3	)	)	PUNCT
ejpam-412	297	1	=	=	SYM
ejpam-412	297	2	e	e	X
ejpam-412	297	3	,	,	PUNCT
ejpam-412	297	4	j	j	PROPN
ejpam-412	297	5	=	=	SYM
ejpam-412	297	6	0	0	NUM
ejpam-412	297	7	,	,	PUNCT
ejpam-412	297	8	1	1	NUM
ejpam-412	297	9	,	,	PUNCT
ejpam-412	297	10	2	2	NUM
ejpam-412	297	11	,	,	PUNCT
ejpam-412	297	12	3	3	NUM
ejpam-412	297	13	,	,	PUNCT
ejpam-412	297	14	4	4	NUM
ejpam-412	297	15	.	.	PUNCT
ejpam-412	297	16	(	(	PUNCT
ejpam-412	297	17	5.23	5.23	NUM
ejpam-412	297	18	)	)	PUNCT
ejpam-412	297	19	applying	apply	VERB
ejpam-412	297	20	the	the	DET
ejpam-412	297	21	operations	operation	NOUN
ejpam-412	297	22	of	of	ADP
ejpam-412	297	23	dt	dt	NOUN
ejpam-412	297	24	to	to	ADP
ejpam-412	297	25	eq	eq	PROPN
ejpam-412	297	26	.	.	PUNCT
ejpam-412	297	27	(	(	PUNCT
ejpam-412	297	28	5.26	5.26	NUM
ejpam-412	297	29	)	)	PUNCT
ejpam-412	297	30	,	,	PUNCT
ejpam-412	297	31	the	the	DET
ejpam-412	297	32	following	follow	VERB
ejpam-412	297	33	recurrence	recurrence	NOUN
ejpam-412	297	34	relation	relation	NOUN
ejpam-412	297	35	is	be	AUX
ejpam-412	297	36	obtained	obtain	VERB
ejpam-412	297	37	y	y	PROPN
ejpam-412	297	38	(	(	PUNCT
ejpam-412	297	39	k+	k+	NOUN
ejpam-412	297	40	10	10	NUM
ejpam-412	297	41	)	)	PUNCT
ejpam-412	297	42	=	=	SYM
ejpam-412	298	1	k	k	X
ejpam-412	298	2	!	!	PUNCT
ejpam-412	298	3	(	(	PUNCT
ejpam-412	298	4	k+10	k+10	NOUN
ejpam-412	298	5	)	)	PUNCT
ejpam-412	298	6	!	!	PUNCT
ejpam-412	299	1	∑k	∑k	PROPN
ejpam-412	299	2	l=0	l=0	PROPN
ejpam-412	299	3	∑l	∑l	PROPN
ejpam-412	299	4	s=0	s=0	X
ejpam-412	299	5	(	(	PUNCT
ejpam-412	299	6	−1)s	−1)s	X
ejpam-412	299	7	s	s	NOUN
ejpam-412	299	8	!	!	PUNCT
ejpam-412	300	1	y	y	PROPN
ejpam-412	300	2	(	(	PUNCT
ejpam-412	300	3	l	l	NOUN
ejpam-412	300	4	−	−	PROPN
ejpam-412	300	5	s)y	s)y	NOUN
ejpam-412	300	6	(	(	PUNCT
ejpam-412	300	7	k−	k−	NOUN
ejpam-412	300	8	l	l	NOUN
ejpam-412	300	9	)	)	PUNCT
ejpam-412	300	10	.	.	PUNCT
ejpam-412	301	1	(	(	PUNCT
ejpam-412	301	2	5.24	5.24	NUM
ejpam-412	301	3	)	)	PUNCT
ejpam-412	301	4	by	by	ADP
ejpam-412	301	5	using	use	VERB
ejpam-412	301	6	eqs	eqs	PROPN
ejpam-412	301	7	.	.	PUNCT
ejpam-412	302	1	(	(	PUNCT
ejpam-412	302	2	2.1	2.1	NUM
ejpam-412	302	3	)	)	PUNCT
ejpam-412	302	4	and	and	CCONJ
ejpam-412	302	5	(	(	PUNCT
ejpam-412	302	6	5.27	5.27	NUM
ejpam-412	302	7	)	)	PUNCT
ejpam-412	302	8	the	the	DET
ejpam-412	302	9	following	follow	VERB
ejpam-412	302	10	transformed	transform	VERB
ejpam-412	302	11	b.c	b.c	PROPN
ejpam-412	302	12	.	.	PROPN
ejpam-412	302	13	’s	’s	X
ejpam-412	302	14	at	at	ADP
ejpam-412	302	15	x	x	X
ejpam-412	302	16	=	=	SYM
ejpam-412	302	17	0	0	NUM
ejpam-412	302	18	can	can	AUX
ejpam-412	302	19	be	be	AUX
ejpam-412	302	20	obtained	obtain	VERB
ejpam-412	302	21	:	:	PUNCT
ejpam-412	302	22	y	y	PROPN
ejpam-412	302	23	(	(	PUNCT
ejpam-412	302	24	0	0	NUM
ejpam-412	302	25	)	)	PUNCT
ejpam-412	302	26	=	=	SYM
ejpam-412	302	27	1	1	NUM
ejpam-412	302	28	,	,	PUNCT
ejpam-412	302	29	y	y	PROPN
ejpam-412	302	30	(	(	PUNCT
ejpam-412	302	31	2	2	NUM
ejpam-412	302	32	)	)	PUNCT
ejpam-412	302	33	=	=	SYM
ejpam-412	302	34	1	1	NUM
ejpam-412	302	35	2	2	NUM
ejpam-412	302	36	!	!	PUNCT
ejpam-412	302	37	,	,	PUNCT
ejpam-412	302	38	y	y	PROPN
ejpam-412	302	39	(	(	PUNCT
ejpam-412	302	40	4	4	NUM
ejpam-412	302	41	)	)	PUNCT
ejpam-412	302	42	=	=	SYM
ejpam-412	302	43	1	1	NUM
ejpam-412	302	44	4	4	NUM
ejpam-412	302	45	!	!	PUNCT
ejpam-412	302	46	,	,	PUNCT
ejpam-412	302	47	y	y	PROPN
ejpam-412	302	48	(	(	PUNCT
ejpam-412	302	49	6	6	NUM
ejpam-412	302	50	)	)	PUNCT
ejpam-412	302	51	=	=	SYM
ejpam-412	302	52	1	1	NUM
ejpam-412	302	53	6	6	NUM
ejpam-412	302	54	!	!	PUNCT
ejpam-412	302	55	,	,	PUNCT
ejpam-412	302	56	y	y	PROPN
ejpam-412	302	57	(	(	PUNCT
ejpam-412	302	58	8)	8)	NUM
ejpam-412	302	59	=	=	SYM
ejpam-412	302	60	1	1	NUM
ejpam-412	302	61	8	8	NUM
ejpam-412	302	62	!	!	PUNCT
ejpam-412	302	63	,	,	PUNCT
ejpam-412	302	64	(	(	PUNCT
ejpam-412	302	65	5.25	5.25	NUM
ejpam-412	302	66	)	)	PUNCT
ejpam-412	302	67	where	where	SCONJ
ejpam-412	302	68	,	,	PUNCT
ejpam-412	302	69	according	accord	VERB
ejpam-412	302	70	to	to	ADP
ejpam-412	302	71	eq	eq	PROPN
ejpam-412	302	72	.	.	PUNCT
ejpam-412	303	1	(	(	PUNCT
ejpam-412	303	2	2.1	2.1	NUM
ejpam-412	303	3	)	)	PUNCT
ejpam-412	303	4	,	,	PUNCT
ejpam-412	303	5	we	we	PRON
ejpam-412	303	6	have	have	VERB
ejpam-412	303	7	a1	a1	NOUN
ejpam-412	303	8	=	=	SYM
ejpam-412	303	9	y	y	PROPN
ejpam-412	303	10	′(0	′(0	PROPN
ejpam-412	303	11	)	)	PUNCT
ejpam-412	304	1	=	=	SYM
ejpam-412	304	2	y	y	PROPN
ejpam-412	304	3	(	(	PUNCT
ejpam-412	304	4	1	1	NUM
ejpam-412	304	5	)	)	PUNCT
ejpam-412	304	6	,	,	PUNCT
ejpam-412	304	7	y	y	PROPN
ejpam-412	304	8	(	(	PUNCT
ejpam-412	304	9	5	5	NUM
ejpam-412	304	10	)	)	PUNCT
ejpam-412	304	11	,	,	PUNCT
ejpam-412	304	12	a2	a2	PROPN
ejpam-412	304	13	=	=	SYM
ejpam-412	304	14	y(iii)(0	y(iii)(0	NUM
ejpam-412	304	15	)	)	PUNCT
ejpam-412	304	16	3	3	NUM
ejpam-412	304	17	!	!	PUNCT
ejpam-412	304	18	=	=	SYM
ejpam-412	305	1	y	y	PROPN
ejpam-412	305	2	(	(	PUNCT
ejpam-412	305	3	3	3	NUM
ejpam-412	305	4	)	)	PUNCT
ejpam-412	305	5	,	,	PUNCT
ejpam-412	305	6	a3	a3	NOUN
ejpam-412	305	7	=	=	SYM
ejpam-412	305	8	y(v)(0	y(v)(0	PROPN
ejpam-412	305	9	)	)	PUNCT
ejpam-412	305	10	5	5	NUM
ejpam-412	305	11	!	!	PUNCT
ejpam-412	305	12	=	=	SYM
ejpam-412	306	1	y	y	PROPN
ejpam-412	306	2	(	(	PUNCT
ejpam-412	306	3	5	5	NUM
ejpam-412	306	4	)	)	PUNCT
ejpam-412	306	5	,	,	PUNCT
ejpam-412	306	6	i.	i.	PROPN
ejpam-412	306	7	abdel	abdel	PROPN
ejpam-412	306	8	-	-	PUNCT
ejpam-412	306	9	halim	halim	PROPN
ejpam-412	306	10	and	and	CCONJ
ejpam-412	306	11	v.	v.	ADP
ejpam-412	306	12	ertürk	ertürk	PROPN
ejpam-412	306	13	/	/	SYM
ejpam-412	306	14	eur	eur	PROPN
ejpam-412	306	15	.	.	PUNCT
ejpam-412	307	1	j.	j.	PROPN
ejpam-412	307	2	pure	pure	PROPN
ejpam-412	307	3	appl	appl	PROPN
ejpam-412	307	4	.	.	PROPN
ejpam-412	307	5	math	math	PROPN
ejpam-412	307	6	,	,	PUNCT
ejpam-412	307	7	2	2	NUM
ejpam-412	307	8	(	(	PUNCT
ejpam-412	307	9	2009	2009	NUM
ejpam-412	307	10	)	)	PUNCT
ejpam-412	307	11	,	,	PUNCT
ejpam-412	307	12	(	(	PUNCT
ejpam-412	307	13	426	426	NUM
ejpam-412	307	14	-	-	NUM
ejpam-412	307	15	447	447	NUM
ejpam-412	307	16	)	)	PUNCT
ejpam-412	307	17	440	440	NUM
ejpam-412	307	18	a4	a4	NOUN
ejpam-412	307	19	=	=	SYM
ejpam-412	307	20	y(vii)(0	y(vii)(0	NUM
ejpam-412	307	21	)	)	PUNCT
ejpam-412	307	22	7	7	NUM
ejpam-412	307	23	!	!	PUNCT
ejpam-412	308	1	=	=	SYM
ejpam-412	308	2	y	y	PROPN
ejpam-412	308	3	(	(	PUNCT
ejpam-412	308	4	7	7	NUM
ejpam-412	308	5	)	)	PUNCT
ejpam-412	308	6	,	,	PUNCT
ejpam-412	308	7	a5	a5	PROPN
ejpam-412	308	8	=	=	PUNCT
ejpam-412	308	9	y(i	y(i	PROPN
ejpam-412	308	10	x)(0	x)(0	NUM
ejpam-412	308	11	)	)	PUNCT
ejpam-412	308	12	9	9	NUM
ejpam-412	308	13	!	!	PUNCT
ejpam-412	309	1	=	=	SYM
ejpam-412	309	2	y	y	PROPN
ejpam-412	309	3	(	(	PUNCT
ejpam-412	309	4	9	9	NUM
ejpam-412	309	5	)	)	PUNCT
ejpam-412	309	6	,	,	PUNCT
ejpam-412	309	7	utilizing	utilize	VERB
ejpam-412	309	8	the	the	DET
ejpam-412	309	9	recurrence	recurrence	NOUN
ejpam-412	309	10	relation	relation	NOUN
ejpam-412	309	11	in	in	ADP
ejpam-412	309	12	eq	eq	ADP
ejpam-412	309	13	.	.	PUNCT
ejpam-412	309	14	(	(	PUNCT
ejpam-412	309	15	5.28	5.28	NUM
ejpam-412	309	16	)	)	PUNCT
ejpam-412	309	17	and	and	CCONJ
ejpam-412	309	18	the	the	DET
ejpam-412	309	19	transformed	transform	VERB
ejpam-412	309	20	b.c	b.c	PROPN
ejpam-412	309	21	.	.	PROPN
ejpam-412	309	22	’s	’s	PART
ejpam-412	309	23	in	in	ADP
ejpam-412	309	24	eq	eq	ADP
ejpam-412	309	25	.	.	PUNCT
ejpam-412	310	1	(	(	PUNCT
ejpam-412	310	2	5.29	5.29	NUM
ejpam-412	310	3	)	)	PUNCT
ejpam-412	310	4	,	,	PUNCT
ejpam-412	310	5	y	y	PROPN
ejpam-412	310	6	(	(	PUNCT
ejpam-412	310	7	k	k	NOUN
ejpam-412	310	8	)	)	PUNCT
ejpam-412	310	9	for	for	ADP
ejpam-412	310	10	k	k	PROPN
ejpam-412	310	11	≥	≥	PROPN
ejpam-412	310	12	10	10	NUM
ejpam-412	310	13	are	be	AUX
ejpam-412	310	14	easily	easily	ADV
ejpam-412	310	15	obtained	obtain	VERB
ejpam-412	310	16	:	:	PUNCT
ejpam-412	310	17	1	1	NUM
ejpam-412	310	18	;	;	PUNCT
ejpam-412	310	19	y	y	PROPN
ejpam-412	310	20	(	(	PUNCT
ejpam-412	310	21	10	10	NUM
ejpam-412	310	22	)	)	PUNCT
ejpam-412	310	23	=	=	SYM
ejpam-412	311	1	1	1	NUM
ejpam-412	311	2	3628800	3628800	NUM
ejpam-412	311	3	,	,	PUNCT
ejpam-412	311	4	y	y	PROPN
ejpam-412	311	5	(	(	PUNCT
ejpam-412	311	6	11	11	NUM
ejpam-412	311	7	)	)	PUNCT
ejpam-412	311	8	=	=	SYM
ejpam-412	311	9	1	1	NUM
ejpam-412	311	10	19958400	19958400	NUM
ejpam-412	311	11	a1	a1	NOUN
ejpam-412	311	12	−	−	PROPN
ejpam-412	311	13	1	1	NUM
ejpam-412	311	14	39916800	39916800	NUM
ejpam-412	311	15	,	,	PUNCT
ejpam-412	311	16	y	y	PROPN
ejpam-412	311	17	(	(	PUNCT
ejpam-412	311	18	12	12	NUM
ejpam-412	311	19	)	)	PUNCT
ejpam-412	311	20	=	=	SYM
ejpam-412	312	1	1	1	NUM
ejpam-412	312	2	159667200	159667200	NUM
ejpam-412	312	3	+	+	CCONJ
ejpam-412	312	4	1	1	NUM
ejpam-412	312	5	239500800	239500800	NUM
ejpam-412	312	6	a2	a2	PROPN
ejpam-412	312	7	1	1	NUM
ejpam-412	312	8	−	−	PROPN
ejpam-412	312	9	1	1	NUM
ejpam-412	312	10	119750400	119750400	NUM
ejpam-412	312	11	a1	a1	NOUN
ejpam-412	312	12	,	,	PUNCT
ejpam-412	312	13	y	y	PROPN
ejpam-412	312	14	(	(	PUNCT
ejpam-412	312	15	13	13	NUM
ejpam-412	312	16	)	)	PUNCT
ejpam-412	312	17	=	=	SYM
ejpam-412	312	18	1	1	NUM
ejpam-412	312	19	518918400	518918400	NUM
ejpam-412	312	20	a2	a2	NOUN
ejpam-412	312	21	+	+	CCONJ
ejpam-412	312	22	1	1	NUM
ejpam-412	312	23	518918400	518918400	NUM
ejpam-412	312	24	a1	a1	NOUN
ejpam-412	312	25	−	−	NOUN
ejpam-412	312	26	1	1	NUM
ejpam-412	312	27	889574400	889574400	NUM
ejpam-412	312	28	−	−	NOUN
ejpam-412	312	29	1	1	NUM
ejpam-412	312	30	1037836800	1037836800	NUM
ejpam-412	312	31	a2	a2	PROPN
ejpam-412	312	32	1	1	NUM
ejpam-412	312	33	,	,	PUNCT
ejpam-412	312	34	y	y	PROPN
ejpam-412	312	35	(	(	PUNCT
ejpam-412	312	36	14	14	NUM
ejpam-412	312	37	)	)	PUNCT
ejpam-412	312	38	=	=	SYM
ejpam-412	313	1	1	1	NUM
ejpam-412	313	2	1037836800	1037836800	NUM
ejpam-412	313	3	+	+	CCONJ
ejpam-412	313	4	1	1	NUM
ejpam-412	313	5	1816214400	1816214400	NUM
ejpam-412	313	6	a1a2	a1a2	INTJ
ejpam-412	313	7	−	−	PROPN
ejpam-412	313	8	1	1	NUM
ejpam-412	313	9	1816214400	1816214400	NUM
ejpam-412	313	10	a2	a2	NOUN
ejpam-412	313	11	−	−	PROPN
ejpam-412	313	12	1	1	NUM
ejpam-412	313	13	2724321600	2724321600	NUM
ejpam-412	313	14	a1	a1	NOUN
ejpam-412	313	15	+	+	CCONJ
ejpam-412	313	16	1	1	NUM
ejpam-412	313	17	7264857600	7264857600	NUM
ejpam-412	313	18	a2	a2	NOUN
ejpam-412	313	19	1	1	NUM
ejpam-412	313	20	...	...	PUNCT
ejpam-412	313	21	and	and	CCONJ
ejpam-412	313	22	so	so	ADV
ejpam-412	313	23	on	on	ADV
ejpam-412	313	24	.	.	PUNCT
ejpam-412	314	1	the	the	DET
ejpam-412	314	2	constants	constant	NOUN
ejpam-412	314	3	a1,a2	a1,a2	PROPN
ejpam-412	314	4	,	,	PUNCT
ejpam-412	314	5	a3	a3	NOUN
ejpam-412	314	6	,	,	PUNCT
ejpam-412	314	7	a4	a4	NOUN
ejpam-412	314	8	and	and	CCONJ
ejpam-412	314	9	a5	a5	PROPN
ejpam-412	314	10	are	be	AUX
ejpam-412	314	11	evaluated	evaluate	VERB
ejpam-412	314	12	from	from	ADP
ejpam-412	314	13	the	the	DET
ejpam-412	314	14	b.c	b.c	PROPN
ejpam-412	314	15	.	.	PROPN
ejpam-412	314	16	’s	’s	AUX
ejpam-412	314	17	given	give	VERB
ejpam-412	314	18	in	in	ADP
ejpam-412	314	19	eq	eq	ADP
ejpam-412	314	20	.	.	PUNCT
ejpam-412	315	1	(	(	PUNCT
ejpam-412	315	2	5.27	5.27	NUM
ejpam-412	315	3	)	)	PUNCT
ejpam-412	315	4	for	for	ADP
ejpam-412	315	5	x	x	SYM
ejpam-412	315	6	=	=	SYM
ejpam-412	315	7	1	1	NUM
ejpam-412	315	8	,	,	PUNCT
ejpam-412	315	9	by	by	ADP
ejpam-412	315	10	taking	take	VERB
ejpam-412	315	11	n	n	NOUN
ejpam-412	315	12	=	=	NUM
ejpam-412	315	13	12	12	NUM
ejpam-412	315	14	,	,	PUNCT
ejpam-412	315	15	to	to	PART
ejpam-412	315	16	obtain	obtain	VERB
ejpam-412	315	17	:	:	PUNCT
ejpam-412	315	18	a1	a1	VERB
ejpam-412	315	19	=	=	SYM
ejpam-412	315	20	1.000000124	1.000000124	NUM
ejpam-412	315	21	,	,	PUNCT
ejpam-412	315	22	a2	a2	PROPN
ejpam-412	315	23	=	=	SYM
ejpam-412	315	24	.9999819650	.9999819650	PROPN
ejpam-412	315	25	,	,	PUNCT
ejpam-412	315	26	a3	a3	NOUN
ejpam-412	315	27	=	=	NOUN
ejpam-412	315	28	1.000157229	1.000157229	NUM
ejpam-412	315	29	,	,	PUNCT
ejpam-412	315	30	a4	a4	NOUN
ejpam-412	315	31	=	=	SYM
ejpam-412	315	32	.9985666714	.9985666714	PROPN
ejpam-412	315	33	,	,	PUNCT
ejpam-412	315	34	a5	a5	PROPN
ejpam-412	315	35	=	=	SYM
ejpam-412	315	36	1.009946626	1.009946626	NUM
ejpam-412	315	37	.	.	PUNCT
ejpam-412	316	1	for	for	ADP
ejpam-412	316	2	n	n	NOUN
ejpam-412	316	3	=	=	SYM
ejpam-412	316	4	17	17	NUM
ejpam-412	316	5	,	,	PUNCT
ejpam-412	316	6	these	these	DET
ejpam-412	316	7	values	value	NOUN
ejpam-412	316	8	are	be	AUX
ejpam-412	316	9	a1	a1	NOUN
ejpam-412	316	10	=	=	SYM
ejpam-412	316	11	.9999698990	.9999698990	PROPN
ejpam-412	316	12	,	,	PUNCT
ejpam-412	316	13	a2	a2	PROPN
ejpam-412	316	14	=	=	PUNCT
ejpam-412	316	15	1.000278188	1.000278188	NUM
ejpam-412	316	16	,	,	PUNCT
ejpam-412	316	17	a3	a3	NOUN
ejpam-412	316	18	=	=	SYM
ejpam-412	316	19	.9973109664	.9973109664	PROPN
ejpam-412	316	20	,	,	PUNCT
ejpam-412	316	21	a4	a4	NOUN
ejpam-412	316	22	=	=	SYM
ejpam-412	316	23	1.023991491	1.023991491	NUM
ejpam-412	316	24	and	and	CCONJ
ejpam-412	317	1	a5	a5	NOUN
ejpam-412	317	2	=	=	SYM
ejpam-412	317	3	.8383579606	.8383579606	PROPN
ejpam-412	317	4	.	.	PUNCT
ejpam-412	318	1	i.	i.	PROPN
ejpam-412	318	2	abdel	abdel	PROPN
ejpam-412	318	3	-	-	PUNCT
ejpam-412	318	4	halim	halim	PROPN
ejpam-412	318	5	and	and	CCONJ
ejpam-412	318	6	v.	v.	ADP
ejpam-412	318	7	ertürk	ertürk	PROPN
ejpam-412	318	8	/	/	SYM
ejpam-412	318	9	eur	eur	PROPN
ejpam-412	318	10	.	.	PUNCT
ejpam-412	319	1	j.	j.	PROPN
ejpam-412	319	2	pure	pure	PROPN
ejpam-412	319	3	appl	appl	PROPN
ejpam-412	319	4	.	.	PROPN
ejpam-412	319	5	math	math	PROPN
ejpam-412	319	6	,	,	PUNCT
ejpam-412	319	7	2	2	NUM
ejpam-412	319	8	(	(	PUNCT
ejpam-412	319	9	2009	2009	NUM
ejpam-412	319	10	)	)	PUNCT
ejpam-412	319	11	,	,	PUNCT
ejpam-412	319	12	(	(	PUNCT
ejpam-412	319	13	426	426	NUM
ejpam-412	319	14	-	-	NUM
ejpam-412	319	15	447	447	NUM
ejpam-412	319	16	)	)	PUNCT
ejpam-412	319	17	441	441	NUM
ejpam-412	319	18	then	then	ADV
ejpam-412	319	19	,	,	PUNCT
ejpam-412	319	20	by	by	ADP
ejpam-412	319	21	using	use	VERB
ejpam-412	319	22	the	the	DET
ejpam-412	319	23	inverse	inverse	NOUN
ejpam-412	319	24	transformation	transformation	NOUN
ejpam-412	319	25	rule	rule	NOUN
ejpam-412	319	26	in	in	ADP
ejpam-412	319	27	eq	eq	PROPN
ejpam-412	319	28	.	.	PUNCT
ejpam-412	320	1	(	(	PUNCT
ejpam-412	320	2	4.2	4.2	NUM
ejpam-412	320	3	)	)	PUNCT
ejpam-412	320	4	,	,	PUNCT
ejpam-412	320	5	we	we	PRON
ejpam-412	320	6	get	get	VERB
ejpam-412	320	7	the	the	DET
ejpam-412	320	8	following	follow	VERB
ejpam-412	320	9	series	series	NOUN
ejpam-412	320	10	solution	solution	NOUN
ejpam-412	320	11	is	be	AUX
ejpam-412	320	12	evaluated	evaluate	VERB
ejpam-412	320	13	up	up	ADP
ejpam-412	320	14	to	to	ADP
ejpam-412	320	15	n	n	NOUN
ejpam-412	320	16	=	=	SYM
ejpam-412	320	17	17	17	NUM
ejpam-412	320	18	:	:	PUNCT
ejpam-412	320	19	numerical	numerical	ADJ
ejpam-412	320	20	results	result	NOUN
ejpam-412	320	21	for	for	ADP
ejpam-412	320	22	non	non	ADJ
ejpam-412	320	23	-	-	ADJ
ejpam-412	320	24	linear	linear	ADJ
ejpam-412	320	25	tenthorder	tenthorder	NOUN
ejpam-412	320	26	bvp	bvp	PROPN
ejpam-412	320	27	,	,	PUNCT
ejpam-412	320	28	the	the	DET
ejpam-412	320	29	differential	differential	ADJ
ejpam-412	320	30	transformation	transformation	NOUN
ejpam-412	320	31	method	method	NOUN
ejpam-412	320	32	(	(	PUNCT
ejpam-412	320	33	dtm	dtm	PROPN
ejpam-412	320	34	)	)	PUNCT
ejpam-412	320	35	with	with	ADP
ejpam-412	320	36	comparison	comparison	NOUN
ejpam-412	320	37	to	to	ADP
ejpam-412	320	38	the	the	DET
ejpam-412	320	39	exact	exact	ADJ
ejpam-412	320	40	solution	solution	NOUN
ejpam-412	320	41	are	be	AUX
ejpam-412	320	42	given	give	VERB
ejpam-412	320	43	in	in	ADP
ejpam-412	320	44	table	table	NOUN
ejpam-412	320	45	4	4	NUM
ejpam-412	320	46	,	,	PUNCT
ejpam-412	320	47	and	and	CCONJ
ejpam-412	320	48	which	which	PRON
ejpam-412	320	49	have	have	AUX
ejpam-412	320	50	been	be	AUX
ejpam-412	320	51	indicated	indicate	VERB
ejpam-412	320	52	in	in	ADP
ejpam-412	320	53	fig	fig	NOUN
ejpam-412	320	54	.	.	PUNCT
ejpam-412	321	1	4	4	X
ejpam-412	321	2	.	.	X
ejpam-412	321	3	table	table	NOUN
ejpam-412	321	4	4	4	NUM
ejpam-412	321	5	:	:	PUNCT
ejpam-412	321	6	comparison	comparison	NOUN
ejpam-412	321	7	of	of	ADP
ejpam-412	321	8	numerical	numerical	ADJ
ejpam-412	321	9	result	result	NOUN
ejpam-412	321	10	of	of	ADP
ejpam-412	321	11	bvp	bvp	PROPN
ejpam-412	321	12	’s	’s	PART
ejpam-412	321	13	(	(	PUNCT
ejpam-412	321	14	5.26)-(5.27	5.26)-(5.27	NUM
ejpam-412	321	15	)	)	PUNCT
ejpam-412	321	16	,	,	PUNCT
ejpam-412	321	17	see	see	VERB
ejpam-412	321	18	fig.4	fig.4	PROPN
ejpam-412	321	19	.	.	PROPN
ejpam-412	321	20	example	example	NOUN
ejpam-412	321	21	5.7	5.7	NUM
ejpam-412	321	22	.	.	PUNCT
ejpam-412	322	1	finally	finally	ADV
ejpam-412	322	2	,	,	PUNCT
ejpam-412	322	3	we	we	PRON
ejpam-412	322	4	consider	consider	VERB
ejpam-412	322	5	the	the	DET
ejpam-412	322	6	non	non	ADJ
ejpam-412	322	7	-	-	ADJ
ejpam-412	322	8	linear	linear	ADJ
ejpam-412	322	9	twelfth	twelfth	ADJ
ejpam-412	322	10	-	-	PUNCT
ejpam-412	322	11	order	order	NOUN
ejpam-412	322	12	bvp	bvp	NOUN
ejpam-412	322	13	[	[	X
ejpam-412	322	14	20	20	NUM
ejpam-412	322	15	]	]	PUNCT
ejpam-412	322	16	y(x	y(x	PROPN
ejpam-412	322	17	ii)(x	ii)(x	PROPN
ejpam-412	322	18	)	)	PUNCT
ejpam-412	322	19	=	=	SYM
ejpam-412	322	20	2ex	2ex	ADJ
ejpam-412	322	21	y2(x	y2(x	PROPN
ejpam-412	322	22	)	)	PUNCT
ejpam-412	322	23	+	+	NUM
ejpam-412	322	24	y(iii)(x	y(iii)(x	NOUN
ejpam-412	322	25	)	)	PUNCT
ejpam-412	322	26	,	,	PUNCT
ejpam-412	322	27	0	0	PUNCT
ejpam-412	322	28	<	<	X
ejpam-412	322	29	x	x	X
ejpam-412	322	30	<	<	X
ejpam-412	322	31	1	1	NUM
ejpam-412	322	32	,	,	PUNCT
ejpam-412	322	33	(	(	PUNCT
ejpam-412	322	34	5.26	5.26	NUM
ejpam-412	322	35	)	)	PUNCT
ejpam-412	322	36	subject	subject	NOUN
ejpam-412	322	37	to	to	ADP
ejpam-412	322	38	the	the	DET
ejpam-412	322	39	boundary	boundary	ADJ
ejpam-412	322	40	conditions	condition	NOUN
ejpam-412	322	41	y(2	y(2	PROPN
ejpam-412	322	42	j)(0	j)(0	ADJ
ejpam-412	322	43	)	)	PUNCT
ejpam-412	322	44	=	=	SYM
ejpam-412	322	45	1	1	NUM
ejpam-412	322	46	,	,	PUNCT
ejpam-412	322	47	j	j	PROPN
ejpam-412	322	48	=	=	SYM
ejpam-412	322	49	0	0	NUM
ejpam-412	322	50	,	,	PUNCT
ejpam-412	322	51	1	1	NUM
ejpam-412	322	52	,	,	PUNCT
ejpam-412	322	53	2	2	NUM
ejpam-412	322	54	,	,	PUNCT
ejpam-412	322	55	3	3	NUM
ejpam-412	322	56	,	,	PUNCT
ejpam-412	322	57	4	4	NUM
ejpam-412	322	58	,	,	PUNCT
ejpam-412	322	59	5	5	NUM
ejpam-412	322	60	,	,	PUNCT
ejpam-412	322	61	y(2	y(2	NOUN
ejpam-412	322	62	j)(1	j)(1	NOUN
ejpam-412	322	63	)	)	PUNCT
ejpam-412	323	1	=	=	SYM
ejpam-412	323	2	e−1	e−1	PROPN
ejpam-412	323	3	,	,	PUNCT
ejpam-412	323	4	j	j	PROPN
ejpam-412	323	5	=	=	SYM
ejpam-412	323	6	0	0	NUM
ejpam-412	323	7	,	,	PUNCT
ejpam-412	323	8	1	1	NUM
ejpam-412	323	9	,	,	PUNCT
ejpam-412	323	10	2	2	NUM
ejpam-412	323	11	,	,	PUNCT
ejpam-412	323	12	3	3	NUM
ejpam-412	323	13	,	,	PUNCT
ejpam-412	323	14	4	4	NUM
ejpam-412	323	15	,	,	PUNCT
ejpam-412	323	16	5	5	NUM
ejpam-412	323	17	.	.	PUNCT
ejpam-412	323	18	(	(	PUNCT
ejpam-412	323	19	5.27	5.27	NUM
ejpam-412	323	20	)	)	PUNCT
ejpam-412	323	21	applying	apply	VERB
ejpam-412	323	22	the	the	DET
ejpam-412	323	23	operations	operation	NOUN
ejpam-412	323	24	of	of	ADP
ejpam-412	323	25	(	(	PUNCT
ejpam-412	323	26	dt	dt	NOUN
ejpam-412	323	27	)	)	PUNCT
ejpam-412	323	28	to	to	ADP
ejpam-412	323	29	eq	eq	NOUN
ejpam-412	323	30	.	.	PUNCT
ejpam-412	323	31	(	(	PUNCT
ejpam-412	323	32	5.31	5.31	NUM
ejpam-412	323	33	)	)	PUNCT
ejpam-412	323	34	,	,	PUNCT
ejpam-412	323	35	the	the	DET
ejpam-412	323	36	following	follow	VERB
ejpam-412	323	37	recurrence	recurrence	NOUN
ejpam-412	323	38	relation	relation	NOUN
ejpam-412	323	39	is	be	AUX
ejpam-412	323	40	i.	i.	PROPN
ejpam-412	323	41	abdel	abdel	PROPN
ejpam-412	323	42	-	-	PUNCT
ejpam-412	323	43	halim	halim	PROPN
ejpam-412	323	44	and	and	CCONJ
ejpam-412	323	45	v.	v.	ADP
ejpam-412	323	46	ertürk	ertürk	PROPN
ejpam-412	323	47	/	/	SYM
ejpam-412	323	48	eur	eur	PROPN
ejpam-412	323	49	.	.	PUNCT
ejpam-412	324	1	j.	j.	PROPN
ejpam-412	324	2	pure	pure	PROPN
ejpam-412	324	3	appl	appl	PROPN
ejpam-412	324	4	.	.	PROPN
ejpam-412	324	5	math	math	PROPN
ejpam-412	324	6	,	,	PUNCT
ejpam-412	324	7	2	2	NUM
ejpam-412	324	8	(	(	PUNCT
ejpam-412	324	9	2009	2009	NUM
ejpam-412	324	10	)	)	PUNCT
ejpam-412	324	11	,	,	PUNCT
ejpam-412	324	12	(	(	PUNCT
ejpam-412	324	13	426	426	NUM
ejpam-412	324	14	-	-	NUM
ejpam-412	324	15	447	447	NUM
ejpam-412	324	16	)	)	PUNCT
ejpam-412	324	17	442	442	NUM
ejpam-412	324	18	obtained	obtain	VERB
ejpam-412	324	19	:	:	PUNCT
ejpam-412	324	20	y	y	PROPN
ejpam-412	324	21	(	(	PUNCT
ejpam-412	324	22	k+	k+	PROPN
ejpam-412	324	23	12	12	NUM
ejpam-412	324	24	)	)	PUNCT
ejpam-412	324	25	=	=	SYM
ejpam-412	325	1	k	k	X
ejpam-412	325	2	!	!	PUNCT
ejpam-412	325	3	(	(	PUNCT
ejpam-412	325	4	k+12	k+12	X
ejpam-412	325	5	)	)	PUNCT
ejpam-412	325	6	!	!	PUNCT
ejpam-412	326	1	h	h	NOUN
ejpam-412	327	1	2	2	X
ejpam-412	328	1	∑k	∑k	PROPN
ejpam-412	328	2	l=0	l=0	PROPN
ejpam-412	328	3	∑l	∑l	PROPN
ejpam-412	328	4	s=0	s=0	PROPN
ejpam-412	328	5	1	1	NUM
ejpam-412	328	6	s	s	NOUN
ejpam-412	328	7	!	!	PUNCT
ejpam-412	329	1	y	y	PROPN
ejpam-412	329	2	(	(	PUNCT
ejpam-412	329	3	l	l	NOUN
ejpam-412	329	4	−	−	PROPN
ejpam-412	329	5	s)y	s)y	NOUN
ejpam-412	329	6	(	(	PUNCT
ejpam-412	329	7	k−	k−	NOUN
ejpam-412	329	8	l	l	NOUN
ejpam-412	329	9	)	)	PUNCT
ejpam-412	330	1	+	+	CCONJ
ejpam-412	330	2	(	(	PUNCT
ejpam-412	330	3	k+	k+	NOUN
ejpam-412	330	4	1)(k+	1)(k+	NUM
ejpam-412	330	5	2)(k+	2)(k+	NUM
ejpam-412	330	6	3)y	3)y	NUM
ejpam-412	330	7	(	(	PUNCT
ejpam-412	330	8	k+	k+	NOUN
ejpam-412	330	9	3	3	X
ejpam-412	330	10	)	)	PUNCT
ejpam-412	330	11	i	i	PRON
ejpam-412	330	12	.	.	PUNCT
ejpam-412	331	1	(	(	PUNCT
ejpam-412	331	2	5.28	5.28	NUM
ejpam-412	331	3	)	)	PUNCT
ejpam-412	331	4	by	by	ADP
ejpam-412	331	5	using	use	VERB
ejpam-412	331	6	eqs	eqs	PROPN
ejpam-412	331	7	.	.	PUNCT
ejpam-412	332	1	(	(	PUNCT
ejpam-412	332	2	2.1	2.1	NUM
ejpam-412	332	3	)	)	PUNCT
ejpam-412	332	4	and	and	CCONJ
ejpam-412	332	5	(	(	PUNCT
ejpam-412	332	6	5.32	5.32	NUM
ejpam-412	332	7	)	)	PUNCT
ejpam-412	333	1	the	the	DET
ejpam-412	333	2	following	follow	VERB
ejpam-412	333	3	transformed	transform	VERB
ejpam-412	333	4	b.c	b.c	PROPN
ejpam-412	333	5	.	.	PROPN
ejpam-412	333	6	’s	’s	X
ejpam-412	333	7	at	at	ADP
ejpam-412	333	8	x	x	X
ejpam-412	333	9	=	=	SYM
ejpam-412	333	10	0	0	NUM
ejpam-412	333	11	can	can	AUX
ejpam-412	333	12	be	be	AUX
ejpam-412	333	13	obtained	obtain	VERB
ejpam-412	333	14	:	:	PUNCT
ejpam-412	333	15	y	y	PROPN
ejpam-412	333	16	(	(	PUNCT
ejpam-412	333	17	0	0	NUM
ejpam-412	333	18	)	)	PUNCT
ejpam-412	333	19	=	=	SYM
ejpam-412	333	20	1	1	NUM
ejpam-412	333	21	,	,	PUNCT
ejpam-412	333	22	y	y	PROPN
ejpam-412	333	23	(	(	PUNCT
ejpam-412	333	24	2	2	NUM
ejpam-412	333	25	)	)	PUNCT
ejpam-412	333	26	=	=	SYM
ejpam-412	333	27	1	1	NUM
ejpam-412	333	28	2	2	NUM
ejpam-412	333	29	!	!	PUNCT
ejpam-412	333	30	,	,	PUNCT
ejpam-412	333	31	y	y	PROPN
ejpam-412	333	32	(	(	PUNCT
ejpam-412	333	33	4	4	NUM
ejpam-412	333	34	)	)	PUNCT
ejpam-412	333	35	=	=	SYM
ejpam-412	333	36	1	1	NUM
ejpam-412	333	37	4	4	NUM
ejpam-412	333	38	!	!	PUNCT
ejpam-412	333	39	,	,	PUNCT
ejpam-412	333	40	y	y	PROPN
ejpam-412	333	41	(	(	PUNCT
ejpam-412	333	42	6	6	NUM
ejpam-412	333	43	)	)	PUNCT
ejpam-412	333	44	=	=	SYM
ejpam-412	333	45	1	1	NUM
ejpam-412	333	46	6	6	NUM
ejpam-412	333	47	!	!	PUNCT
ejpam-412	333	48	,	,	PUNCT
ejpam-412	333	49	y	y	PROPN
ejpam-412	333	50	(	(	PUNCT
ejpam-412	333	51	8)	8)	NUM
ejpam-412	333	52	=	=	SYM
ejpam-412	333	53	1	1	NUM
ejpam-412	333	54	8	8	NUM
ejpam-412	333	55	!	!	PUNCT
ejpam-412	333	56	,	,	PUNCT
ejpam-412	333	57	y	y	PROPN
ejpam-412	333	58	(	(	PUNCT
ejpam-412	333	59	10	10	NUM
ejpam-412	333	60	)	)	PUNCT
ejpam-412	333	61	=	=	SYM
ejpam-412	333	62	1	1	NUM
ejpam-412	333	63	10	10	NUM
ejpam-412	333	64	!	!	PUNCT
ejpam-412	334	1	,	,	PUNCT
ejpam-412	334	2	(	(	PUNCT
ejpam-412	334	3	5.29	5.29	NUM
ejpam-412	334	4	)	)	PUNCT
ejpam-412	334	5	where	where	SCONJ
ejpam-412	334	6	,	,	PUNCT
ejpam-412	334	7	according	accord	VERB
ejpam-412	334	8	to	to	ADP
ejpam-412	334	9	eq	eq	PROPN
ejpam-412	334	10	.	.	PUNCT
ejpam-412	335	1	(	(	PUNCT
ejpam-412	335	2	2.1	2.1	NUM
ejpam-412	335	3	)	)	PUNCT
ejpam-412	335	4	,	,	PUNCT
ejpam-412	335	5	we	we	PRON
ejpam-412	335	6	have	have	VERB
ejpam-412	335	7	y	y	PROPN
ejpam-412	335	8	(	(	PUNCT
ejpam-412	335	9	1	1	NUM
ejpam-412	335	10	)	)	PUNCT
ejpam-412	335	11	=	=	NOUN
ejpam-412	335	12	a1	a1	NOUN
ejpam-412	335	13	=	=	SYM
ejpam-412	335	14	y	y	PROPN
ejpam-412	335	15	′(0	′(0	PROPN
ejpam-412	335	16	)	)	PUNCT
ejpam-412	335	17	,	,	PUNCT
ejpam-412	335	18	y	y	PROPN
ejpam-412	335	19	(	(	PUNCT
ejpam-412	335	20	3	3	NUM
ejpam-412	335	21	)	)	PUNCT
ejpam-412	335	22	=	=	SYM
ejpam-412	335	23	a2	a2	PROPN
ejpam-412	335	24	=	=	SYM
ejpam-412	335	25	y(iii)(0	y(iii)(0	NUM
ejpam-412	335	26	)	)	PUNCT
ejpam-412	335	27	3	3	NUM
ejpam-412	335	28	!	!	NUM
ejpam-412	335	29	,	,	PUNCT
ejpam-412	336	1	y	y	PROPN
ejpam-412	336	2	(	(	PUNCT
ejpam-412	336	3	5	5	NUM
ejpam-412	336	4	)	)	PUNCT
ejpam-412	336	5	=	=	NOUN
ejpam-412	336	6	a3	a3	NOUN
ejpam-412	336	7	=	=	SYM
ejpam-412	336	8	y(v)(0	y(v)(0	PROPN
ejpam-412	336	9	)	)	PUNCT
ejpam-412	336	10	5	5	NUM
ejpam-412	336	11	!	!	NUM
ejpam-412	336	12	,	,	PUNCT
ejpam-412	336	13	y	y	PROPN
ejpam-412	336	14	(	(	PUNCT
ejpam-412	336	15	7	7	NUM
ejpam-412	336	16	)	)	PUNCT
ejpam-412	336	17	=	=	SYM
ejpam-412	336	18	a4	a4	NOUN
ejpam-412	336	19	=	=	SYM
ejpam-412	336	20	y(vii)(0	y(vii)(0	NUM
ejpam-412	336	21	)	)	PUNCT
ejpam-412	336	22	7	7	NUM
ejpam-412	336	23	!	!	NUM
ejpam-412	336	24	,	,	PUNCT
ejpam-412	336	25	y	y	PROPN
ejpam-412	336	26	(	(	PUNCT
ejpam-412	336	27	9	9	NUM
ejpam-412	336	28	)	)	PUNCT
ejpam-412	336	29	=	=	NOUN
ejpam-412	336	30	a5	a5	PROPN
ejpam-412	336	31	=	=	PUNCT
ejpam-412	336	32	y(i	y(i	PROPN
ejpam-412	336	33	x)(0	x)(0	NUM
ejpam-412	336	34	)	)	PUNCT
ejpam-412	336	35	9	9	NUM
ejpam-412	336	36	!	!	NUM
ejpam-412	336	37	,	,	PUNCT
ejpam-412	336	38	y	y	PROPN
ejpam-412	336	39	(	(	PUNCT
ejpam-412	336	40	11	11	NUM
ejpam-412	336	41	)	)	PUNCT
ejpam-412	336	42	=	=	SYM
ejpam-412	336	43	a6	a6	NOUN
ejpam-412	336	44	=	=	SYM
ejpam-412	336	45	y(x	y(x	PROPN
ejpam-412	336	46	i)(0	i)(0	NUM
ejpam-412	336	47	)	)	PUNCT
ejpam-412	336	48	11	11	NUM
ejpam-412	336	49	!	!	PUNCT
ejpam-412	336	50	.	.	PUNCT
ejpam-412	337	1	utilizing	utilize	VERB
ejpam-412	337	2	the	the	DET
ejpam-412	337	3	recurrence	recurrence	NOUN
ejpam-412	337	4	relation	relation	NOUN
ejpam-412	337	5	in	in	ADP
ejpam-412	337	6	eq	eq	ADP
ejpam-412	337	7	.	.	PUNCT
ejpam-412	338	1	(	(	PUNCT
ejpam-412	338	2	5.33	5.33	NUM
ejpam-412	338	3	)	)	PUNCT
ejpam-412	338	4	and	and	CCONJ
ejpam-412	338	5	the	the	DET
ejpam-412	338	6	transformed	transform	VERB
ejpam-412	338	7	b.c	b.c	PROPN
ejpam-412	338	8	.	.	PROPN
ejpam-412	338	9	’s	’s	PART
ejpam-412	338	10	in	in	ADP
ejpam-412	338	11	eq	eq	ADP
ejpam-412	338	12	.	.	PUNCT
ejpam-412	339	1	(	(	PUNCT
ejpam-412	339	2	5.34	5.34	NUM
ejpam-412	339	3	)	)	PUNCT
ejpam-412	339	4	,	,	PUNCT
ejpam-412	339	5	y	y	PROPN
ejpam-412	339	6	(	(	PUNCT
ejpam-412	339	7	k	k	NOUN
ejpam-412	339	8	)	)	PUNCT
ejpam-412	339	9	for	for	SCONJ
ejpam-412	339	10	k	k	PROPN
ejpam-412	339	11	≥	≥	NUM
ejpam-412	339	12	12	12	NUM
ejpam-412	339	13	are	be	AUX
ejpam-412	339	14	easily	easily	ADV
ejpam-412	339	15	obtained	obtain	VERB
ejpam-412	339	16	:	:	PUNCT
ejpam-412	339	17	y	y	PROPN
ejpam-412	339	18	(	(	PUNCT
ejpam-412	339	19	12	12	NUM
ejpam-412	339	20	)	)	PUNCT
ejpam-412	339	21	=	=	SYM
ejpam-412	340	1	1	1	NUM
ejpam-412	340	2	239500800	239500800	NUM
ejpam-412	340	3	+	+	CCONJ
ejpam-412	340	4	1	1	NUM
ejpam-412	340	5	79833600	79833600	NUM
ejpam-412	340	6	a2	a2	NOUN
ejpam-412	340	7	,	,	PUNCT
ejpam-412	340	8	y	y	PROPN
ejpam-412	340	9	(	(	PUNCT
ejpam-412	340	10	13	13	NUM
ejpam-412	340	11	)	)	PUNCT
ejpam-412	340	12	=	=	SYM
ejpam-412	340	13	1	1	NUM
ejpam-412	340	14	2075673600	2075673600	NUM
ejpam-412	340	15	+	+	CCONJ
ejpam-412	340	16	1	1	NUM
ejpam-412	340	17	1556755200	1556755200	NUM
ejpam-412	340	18	a1	a1	NOUN
ejpam-412	340	19	,	,	PUNCT
ejpam-412	340	20	y	y	PROPN
ejpam-412	340	21	(	(	PUNCT
ejpam-412	340	22	14	14	NUM
ejpam-412	340	23	)	)	PUNCT
ejpam-412	340	24	=	=	SYM
ejpam-412	340	25	1	1	NUM
ejpam-412	340	26	14529715200	14529715200	NUM
ejpam-412	340	27	+	+	CCONJ
ejpam-412	340	28	1	1	NUM
ejpam-412	340	29	10897286400	10897286400	NUM
ejpam-412	340	30	a1	a1	NOUN
ejpam-412	340	31	+	+	CCONJ
ejpam-412	340	32	1	1	NUM
ejpam-412	340	33	21794572800	21794572800	NUM
ejpam-412	340	34	a2	a2	PROPN
ejpam-412	340	35	1	1	NUM
ejpam-412	340	36	+	+	CCONJ
ejpam-412	340	37	1	1	NUM
ejpam-412	340	38	726485760	726485760	NUM
ejpam-412	340	39	a3	a3	NOUN
ejpam-412	340	40	,	,	PUNCT
ejpam-412	340	41	y	y	PROPN
ejpam-412	340	42	(	(	PUNCT
ejpam-412	340	43	15	15	NUM
ejpam-412	340	44	)	)	PUNCT
ejpam-412	340	45	=	=	SYM
ejpam-412	340	46	1	1	NUM
ejpam-412	340	47	87178291200	87178291200	NUM
ejpam-412	340	48	+	+	CCONJ
ejpam-412	340	49	1	1	NUM
ejpam-412	340	50	54486432000	54486432000	NUM
ejpam-412	340	51	a1	a1	NOUN
ejpam-412	340	52	+	+	CCONJ
ejpam-412	340	53	1	1	NUM
ejpam-412	340	54	108972864000	108972864000	NUM
ejpam-412	340	55	a2	a2	NOUN
ejpam-412	340	56	1	1	NUM
ejpam-412	340	57	+	+	CCONJ
ejpam-412	340	58	1	1	NUM
ejpam-412	340	59	54486432000	54486432000	NUM
ejpam-412	340	60	a2	a2	NOUN
ejpam-412	340	61	,	,	PUNCT
ejpam-412	340	62	y	y	PROPN
ejpam-412	340	63	(	(	PUNCT
ejpam-412	340	64	16	16	NUM
ejpam-412	340	65	)	)	PUNCT
ejpam-412	340	66	=	=	SYM
ejpam-412	341	1	1	1	NUM
ejpam-412	341	2	498161664000	498161664000	NUM
ejpam-412	341	3	+	+	CCONJ
ejpam-412	341	4	1	1	NUM
ejpam-412	341	5	326918592000	326918592000	NUM
ejpam-412	341	6	a1	a1	NOUN
ejpam-412	341	7	+	+	CCONJ
ejpam-412	341	8	1	1	NUM
ejpam-412	341	9	871782912000	871782912000	NUM
ejpam-412	341	10	a2	a2	NOUN
ejpam-412	341	11	1	1	NUM
ejpam-412	341	12	+	+	CCONJ
ejpam-412	341	13	1	1	NUM
ejpam-412	341	14	217945728000	217945728000	NUM
ejpam-412	341	15	a2	a2	NOUN
ejpam-412	341	16	+	+	CCONJ
ejpam-412	341	17	1	1	NUM
ejpam-412	341	18	217945728000	217945728000	NUM
ejpam-412	341	19	a1a2	a1a2	VERB
ejpam-412	341	20	+	+	NUM
ejpam-412	341	21	1	1	NUM
ejpam-412	341	22	4151347200	4151347200	NUM
ejpam-412	341	23	a4	a4	NOUN
ejpam-412	341	24	,	,	PUNCT
ejpam-412	341	25	...	...	PUNCT
ejpam-412	341	26	i.	i.	PROPN
ejpam-412	341	27	abdel	abdel	PROPN
ejpam-412	341	28	-	-	PUNCT
ejpam-412	341	29	halim	halim	PROPN
ejpam-412	341	30	and	and	CCONJ
ejpam-412	341	31	v.	v.	ADP
ejpam-412	341	32	ertürk	ertürk	PROPN
ejpam-412	341	33	/	/	SYM
ejpam-412	341	34	eur	eur	PROPN
ejpam-412	341	35	.	.	PUNCT
ejpam-412	342	1	j.	j.	PROPN
ejpam-412	342	2	pure	pure	PROPN
ejpam-412	342	3	appl	appl	PROPN
ejpam-412	342	4	.	.	PROPN
ejpam-412	342	5	math	math	PROPN
ejpam-412	342	6	,	,	PUNCT
ejpam-412	342	7	2	2	NUM
ejpam-412	342	8	(	(	PUNCT
ejpam-412	342	9	2009	2009	NUM
ejpam-412	342	10	)	)	PUNCT
ejpam-412	342	11	,	,	PUNCT
ejpam-412	342	12	(	(	PUNCT
ejpam-412	342	13	426	426	NUM
ejpam-412	342	14	-	-	NUM
ejpam-412	342	15	447	447	NUM
ejpam-412	342	16	)	)	PUNCT
ejpam-412	342	17	443	443	NUM
ejpam-412	342	18	and	and	CCONJ
ejpam-412	342	19	so	so	ADV
ejpam-412	342	20	on	on	ADV
ejpam-412	342	21	.	.	PUNCT
ejpam-412	343	1	the	the	DET
ejpam-412	343	2	constants	constant	NOUN
ejpam-412	343	3	a1,a2	a1,a2	PROPN
ejpam-412	343	4	,	,	PUNCT
ejpam-412	343	5	a3	a3	NOUN
ejpam-412	343	6	,	,	PUNCT
ejpam-412	343	7	a4	a4	NOUN
ejpam-412	343	8	,	,	PUNCT
ejpam-412	343	9	a5	a5	PROPN
ejpam-412	343	10	and	and	CCONJ
ejpam-412	343	11	a6	a6	NOUN
ejpam-412	343	12	are	be	AUX
ejpam-412	343	13	evaluated	evaluate	VERB
ejpam-412	343	14	from	from	ADP
ejpam-412	343	15	the	the	DET
ejpam-412	343	16	b.c	b.c	PROPN
ejpam-412	343	17	.	.	PROPN
ejpam-412	343	18	’s	’s	AUX
ejpam-412	343	19	given	give	VERB
ejpam-412	343	20	in	in	ADP
ejpam-412	343	21	eq	eq	ADP
ejpam-412	343	22	.	.	PUNCT
ejpam-412	344	1	(	(	PUNCT
ejpam-412	344	2	5.32	5.32	NUM
ejpam-412	344	3	)	)	PUNCT
ejpam-412	344	4	for	for	ADP
ejpam-412	344	5	x	x	SYM
ejpam-412	344	6	=	=	NOUN
ejpam-412	344	7	1	1	NUM
ejpam-412	344	8	,	,	PUNCT
ejpam-412	344	9	by	by	ADP
ejpam-412	344	10	taking	take	VERB
ejpam-412	344	11	n	n	X
ejpam-412	344	12	=	=	NUM
ejpam-412	344	13	16	16	NUM
ejpam-412	344	14	,	,	PUNCT
ejpam-412	344	15	to	to	PART
ejpam-412	344	16	obtain	obtain	VERB
ejpam-412	344	17	:	:	PUNCT
ejpam-412	344	18	a1	a1	NOUN
ejpam-412	344	19	=	=	NOUN
ejpam-412	344	20	−0.9999999967	−0.9999999967	PROPN
ejpam-412	344	21	,	,	PUNCT
ejpam-412	344	22	a2	a2	PROPN
ejpam-412	344	23	=	=	SYM
ejpam-412	344	24	−0.1666666720	−0.1666666720	PROPN
ejpam-412	344	25	,	,	PUNCT
ejpam-412	344	26	a3	a3	NOUN
ejpam-412	344	27	=	=	SYM
ejpam-412	344	28	−0.0083333307	−0.0083333307	PROPN
ejpam-412	344	29	,	,	PUNCT
ejpam-412	344	30	a4	a4	NOUN
ejpam-412	344	31	=	=	SYM
ejpam-412	344	32	−0.0001984133	−0.0001984133	NOUN
ejpam-412	344	33	,	,	PUNCT
ejpam-412	344	34	a5	a5	PROPN
ejpam-412	344	35	=	=	SYM
ejpam-412	344	36	−0.0000027557	−0.0000027557	NOUN
ejpam-412	344	37	,	,	PUNCT
ejpam-412	344	38	a5	a5	PROPN
ejpam-412	344	39	=	=	PUNCT
ejpam-412	344	40	−0.0000000251	−0.0000000251	NOUN
ejpam-412	344	41	then	then	ADV
ejpam-412	344	42	,	,	PUNCT
ejpam-412	344	43	by	by	ADP
ejpam-412	344	44	using	use	VERB
ejpam-412	344	45	the	the	DET
ejpam-412	344	46	inverse	inverse	NOUN
ejpam-412	344	47	transformation	transformation	NOUN
ejpam-412	344	48	rule	rule	NOUN
ejpam-412	344	49	in	in	ADP
ejpam-412	344	50	eq	eq	PROPN
ejpam-412	344	51	.	.	PUNCT
ejpam-412	345	1	(	(	PUNCT
ejpam-412	345	2	4.2	4.2	NUM
ejpam-412	345	3	)	)	PUNCT
ejpam-412	345	4	,	,	PUNCT
ejpam-412	345	5	we	we	PRON
ejpam-412	345	6	get	get	VERB
ejpam-412	345	7	the	the	DET
ejpam-412	345	8	following	follow	VERB
ejpam-412	345	9	series	series	NOUN
ejpam-412	345	10	solution	solution	NOUN
ejpam-412	345	11	is	be	AUX
ejpam-412	345	12	evaluated	evaluate	VERB
ejpam-412	345	13	up	up	ADP
ejpam-412	345	14	to	to	ADP
ejpam-412	345	15	n	n	NOUN
ejpam-412	345	16	=	=	SYM
ejpam-412	345	17	16	16	NUM
ejpam-412	345	18	:	:	PUNCT
ejpam-412	345	19	numerical	numerical	ADJ
ejpam-412	345	20	results	result	NOUN
ejpam-412	345	21	for	for	ADP
ejpam-412	345	22	non	non	ADJ
ejpam-412	345	23	-	-	ADJ
ejpam-412	345	24	linear	linear	ADJ
ejpam-412	345	25	twelfthorder	twelfthorder	NOUN
ejpam-412	345	26	bvp	bvp	NOUN
ejpam-412	345	27	,	,	PUNCT
ejpam-412	345	28	the	the	DET
ejpam-412	345	29	differential	differential	ADJ
ejpam-412	345	30	transformation	transformation	NOUN
ejpam-412	345	31	method	method	NOUN
ejpam-412	345	32	dtm	dtm	PROPN
ejpam-412	345	33	with	with	ADP
ejpam-412	345	34	comparison	comparison	NOUN
ejpam-412	345	35	to	to	ADP
ejpam-412	345	36	the	the	DET
ejpam-412	345	37	exact	exact	ADJ
ejpam-412	345	38	solution	solution	NOUN
ejpam-412	345	39	are	be	AUX
ejpam-412	345	40	given	give	VERB
ejpam-412	345	41	in	in	ADP
ejpam-412	345	42	table	table	NOUN
ejpam-412	345	43	5	5	NUM
ejpam-412	345	44	,	,	PUNCT
ejpam-412	345	45	and	and	CCONJ
ejpam-412	345	46	which	which	PRON
ejpam-412	345	47	have	have	AUX
ejpam-412	345	48	been	be	AUX
ejpam-412	345	49	indicated	indicate	VERB
ejpam-412	345	50	in	in	ADP
ejpam-412	345	51	fig	fig	NOUN
ejpam-412	345	52	.	.	PUNCT
ejpam-412	346	1	5	5	X
ejpam-412	346	2	.	.	X
ejpam-412	346	3	table	table	NOUN
ejpam-412	346	4	:	:	PUNCT
ejpam-412	346	5	5	5	NUM
ejpam-412	346	6	comparison	comparison	NOUN
ejpam-412	346	7	of	of	ADP
ejpam-412	346	8	numerical	numerical	ADJ
ejpam-412	346	9	result	result	NOUN
ejpam-412	346	10	of	of	ADP
ejpam-412	346	11	bvp	bvp	PROPN
ejpam-412	346	12	’s	’s	PART
ejpam-412	346	13	(	(	PUNCT
ejpam-412	346	14	5.31)-(5.32	5.31)-(5.32	NUM
ejpam-412	346	15	)	)	PUNCT
ejpam-412	346	16	,	,	PUNCT
ejpam-412	346	17	see	see	VERB
ejpam-412	346	18	fig.5	fig.5	PROPN
ejpam-412	346	19	.	.	PUNCT
ejpam-412	346	20	i.	i.	PROPN
ejpam-412	346	21	abdel	abdel	PROPN
ejpam-412	346	22	-	-	PUNCT
ejpam-412	346	23	halim	halim	PROPN
ejpam-412	346	24	and	and	CCONJ
ejpam-412	346	25	v.	v.	ADP
ejpam-412	346	26	ertürk	ertürk	PROPN
ejpam-412	346	27	/	/	SYM
ejpam-412	346	28	eur	eur	PROPN
ejpam-412	346	29	.	.	PUNCT
ejpam-412	347	1	j.	j.	PROPN
ejpam-412	347	2	pure	pure	PROPN
ejpam-412	347	3	appl	appl	PROPN
ejpam-412	347	4	.	.	PROPN
ejpam-412	347	5	math	math	PROPN
ejpam-412	347	6	,	,	PUNCT
ejpam-412	347	7	2	2	NUM
ejpam-412	347	8	(	(	PUNCT
ejpam-412	347	9	2009	2009	NUM
ejpam-412	347	10	)	)	PUNCT
ejpam-412	347	11	,	,	PUNCT
ejpam-412	347	12	(	(	PUNCT
ejpam-412	347	13	426	426	NUM
ejpam-412	347	14	-	-	NUM
ejpam-412	347	15	447	447	NUM
ejpam-412	347	16	)	)	PUNCT
ejpam-412	347	17	444	444	NUM
ejpam-412	347	18	references	reference	NOUN
ejpam-412	347	19	445	445	NUM
ejpam-412	347	20	6	6	NUM
ejpam-412	347	21	.	.	PUNCT
ejpam-412	347	22	conclusion	conclusion	VERB
ejpam-412	347	23	the	the	DET
ejpam-412	347	24	computations	computation	NOUN
ejpam-412	347	25	associated	associate	VERB
ejpam-412	347	26	with	with	ADP
ejpam-412	347	27	the	the	DET
ejpam-412	347	28	examples	example	NOUN
ejpam-412	347	29	discussed	discuss	VERB
ejpam-412	347	30	above	above	ADV
ejpam-412	347	31	were	be	AUX
ejpam-412	347	32	performed	perform	VERB
ejpam-412	347	33	by	by	ADP
ejpam-412	347	34	using	use	VERB
ejpam-412	347	35	maple	maple	NOUN
ejpam-412	347	36	4	4	NUM
ejpam-412	347	37	.	.	PUNCT
ejpam-412	348	1	the	the	DET
ejpam-412	348	2	existence	existence	NOUN
ejpam-412	348	3	and	and	CCONJ
ejpam-412	348	4	uniqueness	uniqueness	NOUN
ejpam-412	348	5	of	of	ADP
ejpam-412	348	6	the	the	DET
ejpam-412	348	7	solution	solution	NOUN
ejpam-412	348	8	is	be	AUX
ejpam-412	348	9	guaranteed	guarantee	VERB
ejpam-412	348	10	by	by	ADP
ejpam-412	348	11	agarwal	agarwal	PROPN
ejpam-412	348	12	’s	’s	PART
ejpam-412	348	13	[	[	X
ejpam-412	348	14	1	1	NUM
ejpam-412	348	15	]	]	PUNCT
ejpam-412	348	16	.	.	PUNCT
ejpam-412	349	1	we	we	PRON
ejpam-412	349	2	first	first	ADV
ejpam-412	349	3	gave	give	VERB
ejpam-412	349	4	the	the	DET
ejpam-412	349	5	definition	definition	NOUN
ejpam-412	349	6	of	of	ADP
ejpam-412	349	7	hobvps	hobvps	NOUN
ejpam-412	349	8	,	,	PUNCT
ejpam-412	349	9	second	second	ADV
ejpam-412	349	10	gave	give	VERB
ejpam-412	349	11	the	the	DET
ejpam-412	349	12	analysis	analysis	NOUN
ejpam-412	349	13	of	of	ADP
ejpam-412	349	14	hobvps	hobvps	NOUN
ejpam-412	349	15	by	by	ADP
ejpam-412	349	16	dtm	dtm	PROPN
ejpam-412	349	17	.	.	PUNCT
ejpam-412	350	1	in	in	ADP
ejpam-412	350	2	above	above	ADP
ejpam-412	350	3	problems	problem	NOUN
ejpam-412	350	4	,	,	PUNCT
ejpam-412	350	5	we	we	PRON
ejpam-412	350	6	gave	give	VERB
ejpam-412	350	7	higher	high	ADJ
ejpam-412	350	8	-	-	PUNCT
ejpam-412	350	9	order	order	NOUN
ejpam-412	350	10	series	series	NOUN
ejpam-412	350	11	solution	solution	NOUN
ejpam-412	350	12	.	.	PUNCT
ejpam-412	351	1	it	it	PRON
ejpam-412	351	2	is	be	AUX
ejpam-412	351	3	shown	show	VERB
ejpam-412	351	4	that	that	SCONJ
ejpam-412	351	5	dtm	dtm	PROPN
ejpam-412	351	6	is	be	AUX
ejpam-412	351	7	a	a	DET
ejpam-412	351	8	very	very	ADV
ejpam-412	351	9	fast	fast	ADJ
ejpam-412	351	10	convergent	convergent	NOUN
ejpam-412	351	11	,	,	PUNCT
ejpam-412	351	12	precise	precise	ADJ
ejpam-412	351	13	and	and	CCONJ
ejpam-412	351	14	cost	cost	VERB
ejpam-412	351	15	efficient	efficient	ADJ
ejpam-412	351	16	tool	tool	NOUN
ejpam-412	351	17	for	for	ADP
ejpam-412	351	18	solving	solve	VERB
ejpam-412	351	19	hobvps	hobvps	NOUN
ejpam-412	351	20	in	in	ADP
ejpam-412	351	21	the	the	DET
ejpam-412	351	22	bounded	bound	VERB
ejpam-412	351	23	domains	domain	NOUN
ejpam-412	351	24	.	.	PUNCT
ejpam-412	352	1	references	reference	NOUN
ejpam-412	352	2	[	[	X
ejpam-412	352	3	1	1	NUM
ejpam-412	352	4	]	]	X
ejpam-412	352	5	r.p	r.p	PROPN
ejpam-412	352	6	.	.	PROPN
ejpam-412	352	7	agarwal	agarwal	PROPN
ejpam-412	352	8	,	,	PUNCT
ejpam-412	352	9	boundary	boundary	ADJ
ejpam-412	352	10	-	-	PUNCT
ejpam-412	352	11	value	value	NOUN
ejpam-412	352	12	problems	problem	NOUN
ejpam-412	352	13	for	for	ADP
ejpam-412	352	14	high	high	ADJ
ejpam-412	352	15	ordinary	ordinary	ADJ
ejpam-412	352	16	differential	differential	ADJ
ejpam-412	352	17	equations	equation	NOUN
ejpam-412	352	18	,	,	PUNCT
ejpam-412	352	19	world	world	NOUN
ejpam-412	352	20	scientific	scientific	PROPN
ejpam-412	352	21	,	,	PUNCT
ejpam-412	352	22	singapore	singapore	PROPN
ejpam-412	352	23	,	,	PUNCT
ejpam-412	352	24	(	(	PUNCT
ejpam-412	352	25	1986	1986	NUM
ejpam-412	352	26	)	)	PUNCT
ejpam-412	352	27	.	.	PUNCT
ejpam-412	353	1	[	[	X
ejpam-412	353	2	2	2	X
ejpam-412	353	3	]	]	PUNCT
ejpam-412	353	4	aytac	aytac	PROPN
ejpam-412	353	5	arıkoğlu	arıkoğlu	PROPN
ejpam-412	353	6	and	and	CCONJ
ejpam-412	353	7	i̇brahim	i̇brahim	PROPN
ejpam-412	353	8	özkol	özkol	NOUN
ejpam-412	353	9	,	,	PUNCT
ejpam-412	353	10	solution	solution	NOUN
ejpam-412	353	11	of	of	ADP
ejpam-412	353	12	boundary	boundary	ADJ
ejpam-412	353	13	value	value	NOUN
ejpam-412	353	14	problems	problem	NOUN
ejpam-412	353	15	for	for	ADP
ejpam-412	353	16	integrodifferential	integrodifferential	ADJ
ejpam-412	353	17	equations	equation	NOUN
ejpam-412	353	18	by	by	ADP
ejpam-412	353	19	using	use	VERB
ejpam-412	353	20	differential	differential	ADJ
ejpam-412	353	21	transform	transform	NOUN
ejpam-412	353	22	method	method	NOUN
ejpam-412	353	23	,	,	PUNCT
ejpam-412	353	24	appllied	appllie	VERB
ejpam-412	353	25	mathematics	mathematic	NOUN
ejpam-412	353	26	and	and	CCONJ
ejpam-412	353	27	computation	computation	NOUN
ejpam-412	353	28	,	,	PUNCT
ejpam-412	353	29	168	168	NUM
ejpam-412	353	30	,	,	PUNCT
ejpam-412	353	31	(	(	PUNCT
ejpam-412	353	32	2005	2005	NUM
ejpam-412	353	33	)	)	PUNCT
ejpam-412	353	34	,	,	PUNCT
ejpam-412	353	35	1145	1145	NUM
ejpam-412	353	36	-	-	SYM
ejpam-412	353	37	1158	1158	NUM
ejpam-412	353	38	.	.	PUNCT
ejpam-412	354	1	references	reference	NOUN
ejpam-412	354	2	446	446	NUM
ejpam-412	354	3	[	[	X
ejpam-412	354	4	3	3	NUM
ejpam-412	354	5	]	]	X
ejpam-412	354	6	f.	f.	PROPN
ejpam-412	354	7	ayaz	ayaz	PROPN
ejpam-412	354	8	,	,	PUNCT
ejpam-412	354	9	solution	solution	NOUN
ejpam-412	354	10	of	of	ADP
ejpam-412	354	11	the	the	DET
ejpam-412	354	12	system	system	NOUN
ejpam-412	354	13	of	of	ADP
ejpam-412	354	14	differential	differential	ADJ
ejpam-412	354	15	equations	equation	NOUN
ejpam-412	354	16	by	by	ADP
ejpam-412	354	17	differential	differential	ADJ
ejpam-412	354	18	transform	transform	NOUN
ejpam-412	354	19	method	method	NOUN
ejpam-412	354	20	,	,	PUNCT
ejpam-412	354	21	appllied	appllie	VERB
ejpam-412	354	22	mathematics	mathematic	NOUN
ejpam-412	354	23	and	and	CCONJ
ejpam-412	354	24	computation	computation	NOUN
ejpam-412	354	25	,	,	PUNCT
ejpam-412	354	26	147,(2004	147,(2004	NUM
ejpam-412	354	27	)	)	PUNCT
ejpam-412	354	28	,	,	PUNCT
ejpam-412	354	29	547	547	NUM
ejpam-412	354	30	-	-	SYM
ejpam-412	354	31	567	567	NUM
ejpam-412	354	32	.	.	PUNCT
ejpam-412	355	1	[	[	X
ejpam-412	355	2	4	4	NUM
ejpam-412	355	3	]	]	X
ejpam-412	355	4	n.	n.	NOUN
ejpam-412	355	5	bildik	bildik	PROPN
ejpam-412	355	6	,	,	PUNCT
ejpam-412	355	7	a.	a.	NOUN
ejpam-412	355	8	konuralp	konuralp	PROPN
ejpam-412	355	9	,	,	PUNCT
ejpam-412	355	10	f.o	f.o	PROPN
ejpam-412	355	11	.	.	PROPN
ejpam-412	355	12	bek	bek	PROPN
ejpam-412	355	13	and	and	CCONJ
ejpam-412	355	14	s.	s.	PROPN
ejpam-412	355	15	küçükarslan	küçükarslan	PROPN
ejpam-412	355	16	,	,	PUNCT
ejpam-412	355	17	solution	solution	NOUN
ejpam-412	355	18	of	of	ADP
ejpam-412	355	19	different	different	ADJ
ejpam-412	355	20	type	type	NOUN
ejpam-412	355	21	of	of	ADP
ejpam-412	355	22	the	the	DET
ejpam-412	355	23	partial	partial	ADJ
ejpam-412	355	24	differential	differential	NOUN
ejpam-412	355	25	equation	equation	NOUN
ejpam-412	355	26	by	by	ADP
ejpam-412	355	27	differential	differential	ADJ
ejpam-412	355	28	transform	transform	NOUN
ejpam-412	355	29	method	method	NOUN
ejpam-412	355	30	and	and	CCONJ
ejpam-412	355	31	adomian	adomian	NOUN
ejpam-412	355	32	’s	’s	PART
ejpam-412	355	33	decomposition	decomposition	NOUN
ejpam-412	355	34	method	method	NOUN
ejpam-412	355	35	,	,	PUNCT
ejpam-412	355	36	appllied	appllie	VERB
ejpam-412	355	37	mathematics	mathematic	NOUN
ejpam-412	355	38	and	and	CCONJ
ejpam-412	355	39	computation,172,(2006	computation,172,(2006	NUM
ejpam-412	355	40	)	)	PUNCT
ejpam-412	355	41	,	,	PUNCT
ejpam-412	355	42	551	551	NUM
ejpam-412	355	43	-	-	SYM
ejpam-412	355	44	567	567	NUM
ejpam-412	355	45	.	.	PUNCT
ejpam-412	356	1	[	[	X
ejpam-412	356	2	5	5	X
ejpam-412	356	3	]	]	PUNCT
ejpam-412	356	4	k.	k.	PROPN
ejpam-412	356	5	bor	bor	PROPN
ejpam-412	356	6	-	-	PUNCT
ejpam-412	356	7	lih	lih	PROPN
ejpam-412	356	8	,	,	PUNCT
ejpam-412	356	9	application	application	NOUN
ejpam-412	356	10	of	of	ADP
ejpam-412	356	11	the	the	DET
ejpam-412	356	12	differential	differential	ADJ
ejpam-412	356	13	transformation	transformation	NOUN
ejpam-412	356	14	method	method	NOUN
ejpam-412	356	15	to	to	ADP
ejpam-412	356	16	the	the	DET
ejpam-412	356	17	solutions	solution	NOUN
ejpam-412	356	18	of	of	ADP
ejpam-412	356	19	the	the	DET
ejpam-412	356	20	free	free	ADJ
ejpam-412	356	21	convection	convection	NOUN
ejpam-412	356	22	problem	problem	NOUN
ejpam-412	356	23	,	,	PUNCT
ejpam-412	356	24	appllied	appllie	VERB
ejpam-412	356	25	mathematics	mathematic	NOUN
ejpam-412	356	26	and	and	CCONJ
ejpam-412	356	27	computation	computation	NOUN
ejpam-412	356	28	,	,	PUNCT
ejpam-412	356	29	165	165	NUM
ejpam-412	356	30	,	,	PUNCT
ejpam-412	356	31	(	(	PUNCT
ejpam-412	356	32	2005	2005	NUM
ejpam-412	356	33	)	)	PUNCT
ejpam-412	356	34	,	,	PUNCT
ejpam-412	356	35	63	63	NUM
ejpam-412	356	36	-	-	SYM
ejpam-412	356	37	79	79	NUM
ejpam-412	356	38	.	.	PUNCT
ejpam-412	357	1	[	[	X
ejpam-412	357	2	6	6	NUM
ejpam-412	357	3	]	]	PUNCT
ejpam-412	357	4	k.	k.	PROPN
ejpam-412	357	5	bor	bor	PROPN
ejpam-412	357	6	-	-	PUNCT
ejpam-412	357	7	lih	lih	ADJ
ejpam-412	357	8	,	,	PUNCT
ejpam-412	357	9	thermal	thermal	ADJ
ejpam-412	357	10	boundary	boundary	ADJ
ejpam-412	357	11	-	-	PUNCT
ejpam-412	357	12	layer	layer	NOUN
ejpam-412	357	13	problems	problem	NOUN
ejpam-412	357	14	in	in	ADP
ejpam-412	357	15	a	a	DET
ejpam-412	357	16	semi	semi	ADJ
ejpam-412	357	17	-	-	ADJ
ejpam-412	357	18	infinite	infinite	ADJ
ejpam-412	357	19	flat	flat	ADJ
ejpam-412	357	20	plate	plate	NOUN
ejpam-412	357	21	by	by	ADP
ejpam-412	357	22	the	the	DET
ejpam-412	357	23	differential	differential	ADJ
ejpam-412	357	24	transformation	transformation	NOUN
ejpam-412	357	25	method	method	NOUN
ejpam-412	357	26	,	,	PUNCT
ejpam-412	357	27	appllied	appllie	VERB
ejpam-412	357	28	mathematics	mathematic	NOUN
ejpam-412	357	29	and	and	CCONJ
ejpam-412	357	30	computation	computation	NOUN
ejpam-412	357	31	,	,	PUNCT
ejpam-412	357	32	150	150	NUM
ejpam-412	357	33	,	,	PUNCT
ejpam-412	357	34	(	(	PUNCT
ejpam-412	357	35	2004	2004	NUM
ejpam-412	357	36	)	)	PUNCT
ejpam-412	357	37	,	,	PUNCT
ejpam-412	357	38	303	303	NUM
ejpam-412	357	39	-	-	SYM
ejpam-412	357	40	320	320	NUM
ejpam-412	357	41	.	.	PUNCT
ejpam-412	358	1	[	[	X
ejpam-412	358	2	7	7	X
ejpam-412	358	3	]	]	X
ejpam-412	358	4	c.	c.	PROPN
ejpam-412	358	5	k.	k.	PROPN
ejpam-412	358	6	chen	chen	PROPN
ejpam-412	358	7	,	,	PUNCT
ejpam-412	358	8	s.	s.	PROPN
ejpam-412	358	9	h.	h.	PROPN
ejpam-412	358	10	ho	ho	PROPN
ejpam-412	358	11	,	,	PUNCT
ejpam-412	358	12	solving	solve	VERB
ejpam-412	358	13	partial	partial	ADJ
ejpam-412	358	14	differential	differential	NOUN
ejpam-412	358	15	eqyation	eqyation	NOUN
ejpam-412	358	16	by	by	ADP
ejpam-412	358	17	differential	differential	ADJ
ejpam-412	358	18	transforma	transforma	NOUN
ejpam-412	358	19	,	,	PUNCT
ejpam-412	358	20	appllied	appllie	VERB
ejpam-412	358	21	mathematics	mathematic	NOUN
ejpam-412	358	22	and	and	CCONJ
ejpam-412	358	23	computation	computation	NOUN
ejpam-412	358	24	,	,	PUNCT
ejpam-412	358	25	106	106	NUM
ejpam-412	358	26	,	,	PUNCT
ejpam-412	358	27	(	(	PUNCT
ejpam-412	358	28	1999	1999	NUM
ejpam-412	358	29	)	)	PUNCT
ejpam-412	358	30	,	,	PUNCT
ejpam-412	358	31	171	171	NUM
ejpam-412	358	32	-	-	SYM
ejpam-412	358	33	179	179	NUM
ejpam-412	358	34	.	.	PUNCT
ejpam-412	359	1	[	[	X
ejpam-412	359	2	8	8	NUM
ejpam-412	359	3	]	]	X
ejpam-412	359	4	c.	c.	PROPN
ejpam-412	359	5	k.	k.	PROPN
ejpam-412	359	6	chen	chen	PROPN
ejpam-412	359	7	,	,	PUNCT
ejpam-412	359	8	s.	s.	PROPN
ejpam-412	359	9	h.	h.	PROPN
ejpam-412	359	10	ho	ho	PROPN
ejpam-412	359	11	,	,	PUNCT
ejpam-412	359	12	application	application	NOUN
ejpam-412	359	13	of	of	ADP
ejpam-412	359	14	diffrential	diffrential	ADJ
ejpam-412	359	15	transformation	transformation	NOUN
ejpam-412	359	16	to	to	AUX
ejpam-412	359	17	eigenvalue	eigenvalue	VERB
ejpam-412	359	18	problems	problem	NOUN
ejpam-412	359	19	,	,	PUNCT
ejpam-412	359	20	appllied	appllie	VERB
ejpam-412	359	21	mathematics	mathematic	NOUN
ejpam-412	359	22	and	and	CCONJ
ejpam-412	359	23	computation	computation	NOUN
ejpam-412	359	24	,	,	PUNCT
ejpam-412	359	25	79	79	NUM
ejpam-412	359	26	,	,	PUNCT
ejpam-412	359	27	(	(	PUNCT
ejpam-412	359	28	1996	1996	NUM
ejpam-412	359	29	)	)	PUNCT
ejpam-412	359	30	,	,	PUNCT
ejpam-412	359	31	173	173	NUM
ejpam-412	359	32	-	-	SYM
ejpam-412	359	33	188	188	NUM
ejpam-412	359	34	.	.	PUNCT
ejpam-412	360	1	[	[	X
ejpam-412	360	2	9	9	NUM
ejpam-412	360	3	]	]	PUNCT
ejpam-412	360	4	c.	c.	PROPN
ejpam-412	360	5	l.	l.	PROPN
ejpam-412	360	6	chen	chen	PROPN
ejpam-412	360	7	,	,	PUNCT
ejpam-412	360	8	y.	y.	PROPN
ejpam-412	360	9	c.	c.	PROPN
ejpam-412	360	10	liu	liu	PROPN
ejpam-412	360	11	,	,	PUNCT
ejpam-412	360	12	solution	solution	NOUN
ejpam-412	360	13	of	of	ADP
ejpam-412	360	14	two	two	NUM
ejpam-412	360	15	point	point	NOUN
ejpam-412	360	16	boundary	boundary	ADJ
ejpam-412	360	17	value	value	NOUN
ejpam-412	360	18	problems	problem	NOUN
ejpam-412	360	19	using	use	VERB
ejpam-412	360	20	the	the	DET
ejpam-412	360	21	differential	differential	ADJ
ejpam-412	360	22	transformation	transformation	NOUN
ejpam-412	360	23	method	method	NOUN
ejpam-412	360	24	,	,	PUNCT
ejpam-412	360	25	journal	journal	NOUN
ejpam-412	360	26	of	of	ADP
ejpam-412	360	27	optimization	optimization	NOUN
ejpam-412	360	28	theory	theory	NOUN
ejpam-412	360	29	and	and	CCONJ
ejpam-412	360	30	applications	application	NOUN
ejpam-412	360	31	,	,	PUNCT
ejpam-412	360	32	99	99	NUM
ejpam-412	360	33	,	,	PUNCT
ejpam-412	360	34	(	(	PUNCT
ejpam-412	360	35	1998	1998	NUM
ejpam-412	360	36	)	)	PUNCT
ejpam-412	360	37	,	,	PUNCT
ejpam-412	360	38	23	23	NUM
ejpam-412	360	39	-	-	SYM
ejpam-412	360	40	35	35	NUM
ejpam-412	360	41	.	.	PUNCT
ejpam-412	361	1	[	[	X
ejpam-412	361	2	10	10	NUM
ejpam-412	361	3	]	]	PUNCT
ejpam-412	361	4	m.	m.	NOUN
ejpam-412	361	5	m.	m.	NOUN
ejpam-412	361	6	chawia	chawia	PROPN
ejpam-412	361	7	and	and	CCONJ
ejpam-412	361	8	c.	c.	PROPN
ejpam-412	361	9	p.	p.	PROPN
ejpam-412	361	10	katti	katti	PROPN
ejpam-412	361	11	,	,	PUNCT
ejpam-412	361	12	finite	finite	ADJ
ejpam-412	361	13	difference	difference	NOUN
ejpam-412	361	14	methods	method	NOUN
ejpam-412	361	15	for	for	ADP
ejpam-412	361	16	two	two	NUM
ejpam-412	361	17	-	-	PUNCT
ejpam-412	361	18	point	point	NOUN
ejpam-412	361	19	boundary	boundary	ADJ
ejpam-412	361	20	value	value	NOUN
ejpam-412	361	21	problem	problem	NOUN
ejpam-412	361	22	involving	involve	VERB
ejpam-412	361	23	higher	high	ADJ
ejpam-412	361	24	order	order	NOUN
ejpam-412	361	25	differential	differential	ADJ
ejpam-412	361	26	equations	equation	NOUN
ejpam-412	361	27	,	,	PUNCT
ejpam-412	361	28	bit	bit	NOUN
ejpam-412	361	29	,	,	PUNCT
ejpam-412	361	30	19	19	NUM
ejpam-412	361	31	,	,	PUNCT
ejpam-412	361	32	(	(	PUNCT
ejpam-412	361	33	1979	1979	NUM
ejpam-412	361	34	)	)	PUNCT
ejpam-412	361	35	,	,	PUNCT
ejpam-412	361	36	27	27	NUM
ejpam-412	361	37	-	-	SYM
ejpam-412	361	38	33	33	NUM
ejpam-412	361	39	.	.	PUNCT
ejpam-412	362	1	[	[	X
ejpam-412	362	2	11	11	NUM
ejpam-412	362	3	]	]	X
ejpam-412	362	4	[	[	X
ejpam-412	362	5	11	11	NUM
ejpam-412	362	6	]	]	PUNCT
ejpam-412	362	7	k.	k.	PROPN
ejpam-412	362	8	djidjeli	djidjeli	PROPN
ejpam-412	362	9	,	,	PUNCT
ejpam-412	362	10	e.h	e.h	PROPN
ejpam-412	362	11	.	.	PROPN
ejpam-412	362	12	twizell	twizell	PROPN
ejpam-412	362	13	and	and	CCONJ
ejpam-412	362	14	a.	a.	PROPN
ejpam-412	362	15	boutayeb	boutayeb	PROPN
ejpam-412	362	16	,	,	PUNCT
ejpam-412	362	17	numerical	numerical	ADJ
ejpam-412	362	18	methods	method	NOUN
ejpam-412	362	19	for	for	ADP
ejpam-412	362	20	special	special	ADJ
ejpam-412	362	21	nonlinear	nonlinear	ADJ
ejpam-412	362	22	boundary	boundary	ADJ
ejpam-412	362	23	-	-	PUNCT
ejpam-412	362	24	value	value	NOUN
ejpam-412	362	25	problems	problem	NOUN
ejpam-412	362	26	of	of	ADP
ejpam-412	362	27	order	order	NOUN
ejpam-412	362	28	2	2	NUM
ejpam-412	362	29	m	m	NOUN
ejpam-412	362	30	,	,	PUNCT
ejpam-412	362	31	journal	journal	NOUN
ejpam-412	362	32	of	of	ADP
ejpam-412	362	33	computational	computational	ADJ
ejpam-412	362	34	and	and	CCONJ
ejpam-412	362	35	applied	applied	ADJ
ejpam-412	362	36	mathematics	mathematic	NOUN
ejpam-412	362	37	,	,	PUNCT
ejpam-412	362	38	47	47	NUM
ejpam-412	362	39	,	,	PUNCT
ejpam-412	362	40	(	(	PUNCT
ejpam-412	362	41	1993	1993	NUM
ejpam-412	362	42	)	)	PUNCT
ejpam-412	362	43	,	,	PUNCT
ejpam-412	362	44	35	35	NUM
ejpam-412	362	45	-	-	SYM
ejpam-412	362	46	45	45	NUM
ejpam-412	362	47	.	.	PUNCT
ejpam-412	363	1	[	[	X
ejpam-412	363	2	12	12	NUM
ejpam-412	363	3	]	]	PUNCT
ejpam-412	363	4	v.s.	v.s.	X
ejpam-412	363	5	ertürk	ertürk	PROPN
ejpam-412	363	6	,	,	PUNCT
ejpam-412	363	7	s.	s.	PROPN
ejpam-412	363	8	momani	momani	PROPN
ejpam-412	363	9	,	,	PUNCT
ejpam-412	363	10	comparing	compare	VERB
ejpam-412	363	11	numerical	numerical	ADJ
ejpam-412	363	12	methods	method	NOUN
ejpam-412	363	13	for	for	ADP
ejpam-412	363	14	solving	solve	VERB
ejpam-412	363	15	fourth	fourth	ADJ
ejpam-412	363	16	-	-	PUNCT
ejpam-412	363	17	order	order	NOUN
ejpam-412	363	18	boundary	boundary	ADJ
ejpam-412	363	19	value	value	NOUN
ejpam-412	363	20	problems	problem	NOUN
ejpam-412	363	21	,	,	PUNCT
ejpam-412	363	22	appllied	appllie	VERB
ejpam-412	363	23	mathematics	mathematic	NOUN
ejpam-412	363	24	and	and	CCONJ
ejpam-412	363	25	computation	computation	NOUN
ejpam-412	363	26	,	,	PUNCT
ejpam-412	363	27	188,2	188,2	NUM
ejpam-412	363	28	,	,	PUNCT
ejpam-412	363	29	(	(	PUNCT
ejpam-412	363	30	2007	2007	NUM
ejpam-412	363	31	)	)	PUNCT
ejpam-412	363	32	1963	1963	NUM
ejpam-412	363	33	-	-	SYM
ejpam-412	363	34	1968	1968	NUM
ejpam-412	363	35	.	.	PUNCT
ejpam-412	364	1	[	[	X
ejpam-412	364	2	13	13	NUM
ejpam-412	364	3	]	]	X
ejpam-412	364	4	i.	i.	PROPN
ejpam-412	364	5	h.	h.	PROPN
ejpam-412	364	6	abdel	abdel	PROPN
ejpam-412	364	7	-	-	PUNCT
ejpam-412	364	8	halim	halim	PROPN
ejpam-412	364	9	hassan	hassan	PROPN
ejpam-412	364	10	,	,	PUNCT
ejpam-412	364	11	different	different	ADJ
ejpam-412	364	12	applications	application	NOUN
ejpam-412	364	13	for	for	ADP
ejpam-412	364	14	the	the	DET
ejpam-412	364	15	differential	differential	ADJ
ejpam-412	364	16	transformation	transformation	NOUN
ejpam-412	364	17	in	in	ADP
ejpam-412	364	18	the	the	DET
ejpam-412	364	19	differential	differential	ADJ
ejpam-412	364	20	equations	equation	NOUN
ejpam-412	364	21	,	,	PUNCT
ejpam-412	364	22	appllied	appllie	VERB
ejpam-412	364	23	mathematics	mathematic	NOUN
ejpam-412	364	24	and	and	CCONJ
ejpam-412	364	25	computation	computation	NOUN
ejpam-412	364	26	,	,	PUNCT
ejpam-412	364	27	129	129	NUM
ejpam-412	364	28	,	,	PUNCT
ejpam-412	364	29	(	(	PUNCT
ejpam-412	364	30	2002	2002	NUM
ejpam-412	364	31	)	)	PUNCT
ejpam-412	364	32	,	,	PUNCT
ejpam-412	364	33	183201	183201	NUM
ejpam-412	364	34	.	.	PUNCT
ejpam-412	365	1	[	[	X
ejpam-412	365	2	14	14	NUM
ejpam-412	365	3	]	]	X
ejpam-412	365	4	i.	i.	PROPN
ejpam-412	365	5	h.	h.	PROPN
ejpam-412	365	6	abdel	abdel	PROPN
ejpam-412	365	7	-	-	PUNCT
ejpam-412	365	8	halim	halim	PROPN
ejpam-412	365	9	hassan	hassan	PROPN
ejpam-412	365	10	,	,	PUNCT
ejpam-412	365	11	on	on	ADP
ejpam-412	365	12	solving	solve	VERB
ejpam-412	365	13	some	some	DET
ejpam-412	365	14	eigenvalue	eigenvalue	ADJ
ejpam-412	365	15	problems	problem	NOUN
ejpam-412	365	16	by	by	ADP
ejpam-412	365	17	using	use	VERB
ejpam-412	365	18	a	a	DET
ejpam-412	365	19	differential	differential	ADJ
ejpam-412	365	20	transformation	transformation	NOUN
ejpam-412	365	21	,	,	PUNCT
ejpam-412	365	22	appllied	appllie	VERB
ejpam-412	365	23	mathematics	mathematic	NOUN
ejpam-412	365	24	and	and	CCONJ
ejpam-412	365	25	computation	computation	NOUN
ejpam-412	365	26	,	,	PUNCT
ejpam-412	365	27	127	127	NUM
ejpam-412	365	28	,	,	PUNCT
ejpam-412	365	29	(	(	PUNCT
ejpam-412	365	30	2002	2002	NUM
ejpam-412	365	31	)	)	PUNCT
ejpam-412	365	32	,	,	PUNCT
ejpam-412	365	33	1	1	NUM
ejpam-412	365	34	-	-	SYM
ejpam-412	365	35	22	22	NUM
ejpam-412	365	36	.	.	PUNCT
ejpam-412	366	1	references	reference	NOUN
ejpam-412	366	2	447	447	NUM
ejpam-412	367	1	[	[	X
ejpam-412	367	2	15	15	NUM
ejpam-412	367	3	]	]	X
ejpam-412	367	4	i.	i.	PROPN
ejpam-412	367	5	h.	h.	PROPN
ejpam-412	367	6	abdel	abdel	PROPN
ejpam-412	367	7	-	-	PUNCT
ejpam-412	367	8	halim	halim	PROPN
ejpam-412	367	9	hassan	hassan	PROPN
ejpam-412	367	10	,	,	PUNCT
ejpam-412	367	11	diffrential	diffrential	ADJ
ejpam-412	367	12	transformation	transformation	NOUN
ejpam-412	367	13	technique	technique	NOUN
ejpam-412	367	14	for	for	ADP
ejpam-412	367	15	solving	solve	VERB
ejpam-412	367	16	higher	high	ADJ
ejpam-412	367	17	-	-	PUNCT
ejpam-412	367	18	order	order	NOUN
ejpam-412	367	19	initial	initial	ADJ
ejpam-412	367	20	value	value	NOUN
ejpam-412	367	21	problems	problem	NOUN
ejpam-412	367	22	,	,	PUNCT
ejpam-412	367	23	appllied	appllie	VERB
ejpam-412	367	24	mathematics	mathematic	NOUN
ejpam-412	367	25	and	and	CCONJ
ejpam-412	367	26	computation	computation	NOUN
ejpam-412	367	27	,	,	PUNCT
ejpam-412	367	28	154	154	NUM
ejpam-412	367	29	,	,	PUNCT
ejpam-412	367	30	(	(	PUNCT
ejpam-412	367	31	2004	2004	NUM
ejpam-412	367	32	)	)	PUNCT
ejpam-412	367	33	,	,	PUNCT
ejpam-412	367	34	299	299	NUM
ejpam-412	367	35	-	-	SYM
ejpam-412	367	36	311	311	NUM
ejpam-412	367	37	.	.	PUNCT
ejpam-412	368	1	[	[	X
ejpam-412	368	2	16	16	NUM
ejpam-412	368	3	]	]	PUNCT
ejpam-412	368	4	m.	m.	NOUN
ejpam-412	368	5	j.	j.	PROPN
ejpam-412	368	6	jang	jang	PROPN
ejpam-412	368	7	,	,	PUNCT
ejpam-412	368	8	c.	c.	PROPN
ejpam-412	368	9	l.	l.	PROPN
ejpam-412	368	10	chen	chen	PROPN
ejpam-412	368	11	,	,	PUNCT
ejpam-412	368	12	y.c	y.c	PROPN
ejpam-412	368	13	.	.	PROPN
ejpam-412	368	14	liu	liu	PROPN
ejpam-412	368	15	,	,	PUNCT
ejpam-412	368	16	on	on	ADP
ejpam-412	368	17	solving	solve	VERB
ejpam-412	368	18	the	the	DET
ejpam-412	368	19	initial	initial	ADJ
ejpam-412	368	20	value	value	NOUN
ejpam-412	368	21	problems	problem	NOUN
ejpam-412	368	22	using	use	VERB
ejpam-412	368	23	the	the	DET
ejpam-412	368	24	differential	differential	ADJ
ejpam-412	368	25	transformation	transformation	NOUN
ejpam-412	368	26	method	method	NOUN
ejpam-412	368	27	,	,	PUNCT
ejpam-412	368	28	appllied	appllie	VERB
ejpam-412	368	29	mathematics	mathematic	NOUN
ejpam-412	368	30	and	and	CCONJ
ejpam-412	368	31	computation	computation	NOUN
ejpam-412	368	32	,	,	PUNCT
ejpam-412	368	33	115	115	NUM
ejpam-412	368	34	,	,	PUNCT
ejpam-412	368	35	(	(	PUNCT
ejpam-412	368	36	2000	2000	NUM
ejpam-412	368	37	)	)	PUNCT
ejpam-412	368	38	,	,	PUNCT
ejpam-412	368	39	145	145	NUM
ejpam-412	368	40	-	-	SYM
ejpam-412	368	41	160	160	NUM
ejpam-412	368	42	.	.	PUNCT
ejpam-412	369	1	[	[	X
ejpam-412	369	2	17	17	NUM
ejpam-412	369	3	]	]	X
ejpam-412	369	4	j.	j.	PROPN
ejpam-412	369	5	m.	m.	PROPN
ejpam-412	369	6	jang	jang	PROPN
ejpam-412	369	7	and	and	CCONJ
ejpam-412	369	8	c.	c.	PROPN
ejpam-412	369	9	l.	l.	PROPN
ejpam-412	369	10	chen	chen	PROPN
ejpam-412	369	11	,	,	PUNCT
ejpam-412	369	12	analysis	analysis	NOUN
ejpam-412	369	13	of	of	ADP
ejpam-412	369	14	the	the	DET
ejpam-412	369	15	response	response	NOUN
ejpam-412	369	16	of	of	ADP
ejpam-412	369	17	a	a	DET
ejpam-412	369	18	strongly	strongly	ADV
ejpam-412	369	19	nonlinear	nonlinear	ADJ
ejpam-412	369	20	damped	damp	VERB
ejpam-412	369	21	system	system	NOUN
ejpam-412	369	22	using	use	VERB
ejpam-412	369	23	a	a	DET
ejpam-412	369	24	differential	differential	ADJ
ejpam-412	369	25	transformation	transformation	NOUN
ejpam-412	369	26	technique	technique	NOUN
ejpam-412	369	27	,	,	PUNCT
ejpam-412	369	28	appllied	appllie	VERB
ejpam-412	369	29	mathematics	mathematic	NOUN
ejpam-412	369	30	and	and	CCONJ
ejpam-412	369	31	computation	computation	NOUN
ejpam-412	369	32	,	,	PUNCT
ejpam-412	369	33	88	88	NUM
ejpam-412	369	34	,	,	PUNCT
ejpam-412	369	35	(	(	PUNCT
ejpam-412	369	36	1997	1997	NUM
ejpam-412	369	37	)	)	PUNCT
ejpam-412	369	38	,	,	PUNCT
ejpam-412	369	39	137	137	NUM
ejpam-412	369	40	-	-	SYM
ejpam-412	369	41	151	151	NUM
ejpam-412	369	42	.	.	PUNCT
ejpam-412	370	1	[	[	X
ejpam-412	370	2	18	18	NUM
ejpam-412	370	3	]	]	X
ejpam-412	370	4	m.malik	m.malik	NOUN
ejpam-412	370	5	and	and	CCONJ
ejpam-412	370	6	h.	h.	PROPN
ejpam-412	370	7	h.	h.	PROPN
ejpam-412	370	8	dang	dang	PROPN
ejpam-412	370	9	,	,	PUNCT
ejpam-412	370	10	vibration	vibration	NOUN
ejpam-412	370	11	analysis	analysis	NOUN
ejpam-412	370	12	of	of	ADP
ejpam-412	370	13	continuous	continuous	ADJ
ejpam-412	370	14	system	system	NOUN
ejpam-412	370	15	by	by	ADP
ejpam-412	370	16	differential	differential	ADJ
ejpam-412	370	17	transformation	transformation	NOUN
ejpam-412	370	18	,	,	PUNCT
ejpam-412	370	19	appllied	appllie	VERB
ejpam-412	370	20	mathematics	mathematic	NOUN
ejpam-412	370	21	and	and	CCONJ
ejpam-412	370	22	computation	computation	NOUN
ejpam-412	370	23	,	,	PUNCT
ejpam-412	370	24	96	96	NUM
ejpam-412	370	25	,	,	PUNCT
ejpam-412	370	26	(	(	PUNCT
ejpam-412	370	27	1998	1998	NUM
ejpam-412	370	28	)	)	PUNCT
ejpam-412	370	29	,	,	PUNCT
ejpam-412	370	30	17	17	NUM
ejpam-412	370	31	-	-	SYM
ejpam-412	370	32	26	26	NUM
ejpam-412	370	33	.	.	PUNCT
ejpam-412	371	1	[	[	X
ejpam-412	371	2	19	19	NUM
ejpam-412	371	3	]	]	PUNCT
ejpam-412	371	4	a.	a.	NOUN
ejpam-412	371	5	m.	m.	PROPN
ejpam-412	371	6	wazwaz	wazwaz	PROPN
ejpam-412	371	7	,	,	PUNCT
ejpam-412	371	8	the	the	DET
ejpam-412	371	9	numerical	numerical	ADJ
ejpam-412	371	10	solution	solution	NOUN
ejpam-412	371	11	of	of	ADP
ejpam-412	371	12	sixth	sixth	ADJ
ejpam-412	371	13	-	-	PUNCT
ejpam-412	371	14	order	order	NOUN
ejpam-412	371	15	boundary	boundary	ADJ
ejpam-412	371	16	value	value	NOUN
ejpam-412	371	17	problems	problem	NOUN
ejpam-412	371	18	by	by	ADP
ejpam-412	371	19	the	the	DET
ejpam-412	371	20	modified	modify	VERB
ejpam-412	371	21	decomposition	decomposition	NOUN
ejpam-412	371	22	method	method	NOUN
ejpam-412	371	23	,	,	PUNCT
ejpam-412	371	24	appllied	appllie	VERB
ejpam-412	371	25	mathematics	mathematic	NOUN
ejpam-412	371	26	and	and	CCONJ
ejpam-412	371	27	computation	computation	NOUN
ejpam-412	371	28	,	,	PUNCT
ejpam-412	371	29	118	118	NUM
ejpam-412	371	30	,	,	PUNCT
ejpam-412	371	31	(	(	PUNCT
ejpam-412	371	32	2001	2001	NUM
ejpam-412	371	33	)	)	PUNCT
ejpam-412	371	34	,	,	PUNCT
ejpam-412	371	35	311	311	NUM
ejpam-412	371	36	-	-	SYM
ejpam-412	371	37	325	325	NUM
ejpam-412	371	38	.	.	PUNCT
ejpam-412	372	1	[	[	X
ejpam-412	372	2	20	20	NUM
ejpam-412	372	3	]	]	PUNCT
ejpam-412	372	4	a.	a.	NOUN
ejpam-412	372	5	m.	m.	PROPN
ejpam-412	372	6	wazwaz	wazwaz	PROPN
ejpam-412	372	7	,	,	PUNCT
ejpam-412	372	8	approximate	approximate	ADJ
ejpam-412	372	9	solution	solution	NOUN
ejpam-412	372	10	to	to	ADP
ejpam-412	372	11	boundary	boundary	ADJ
ejpam-412	372	12	value	value	NOUN
ejpam-412	372	13	problems	problem	NOUN
ejpam-412	372	14	of	of	ADP
ejpam-412	372	15	higher	high	ADJ
ejpam-412	372	16	order	order	NOUN
ejpam-412	372	17	by	by	ADP
ejpam-412	372	18	the	the	DET
ejpam-412	372	19	modified	modify	VERB
ejpam-412	372	20	decomposition	decomposition	NOUN
ejpam-412	372	21	method	method	NOUN
ejpam-412	372	22	,	,	PUNCT
ejpam-412	372	23	computer	computer	NOUN
ejpam-412	372	24	mathematics	mathematic	NOUN
ejpam-412	372	25	with	with	ADP
ejpam-412	372	26	applications	application	NOUN
ejpam-412	372	27	,	,	PUNCT
ejpam-412	372	28	40	40	NUM
ejpam-412	372	29	,	,	PUNCT
ejpam-412	372	30	(	(	PUNCT
ejpam-412	372	31	2000	2000	NUM
ejpam-412	372	32	)	)	PUNCT
ejpam-412	372	33	,	,	PUNCT
ejpam-412	372	34	679	679	NUM
ejpam-412	372	35	-	-	SYM
ejpam-412	372	36	691	691	NUM
ejpam-412	372	37	.	.	PUNCT
ejpam-412	373	1	[	[	X
ejpam-412	373	2	21	21	NUM
ejpam-412	373	3	]	]	PUNCT
ejpam-412	373	4	a.	a.	NOUN
ejpam-412	373	5	m.	m.	PROPN
ejpam-412	373	6	wazwaz	wazwaz	PROPN
ejpam-412	373	7	,	,	PUNCT
ejpam-412	373	8	the	the	DET
ejpam-412	373	9	numerical	numerical	ADJ
ejpam-412	373	10	solution	solution	NOUN
ejpam-412	373	11	of	of	ADP
ejpam-412	373	12	fifth	fifth	ADJ
ejpam-412	373	13	-	-	PUNCT
ejpam-412	373	14	order	order	NOUN
ejpam-412	373	15	boundary	boundary	ADJ
ejpam-412	373	16	value	value	NOUN
ejpam-412	373	17	problems	problem	NOUN
ejpam-412	373	18	by	by	ADP
ejpam-412	373	19	the	the	DET
ejpam-412	373	20	decomposition	decomposition	NOUN
ejpam-412	373	21	method	method	NOUN
ejpam-412	373	22	,	,	PUNCT
ejpam-412	373	23	appllied	appllie	VERB
ejpam-412	373	24	mathematics	mathematic	NOUN
ejpam-412	373	25	and	and	CCONJ
ejpam-412	373	26	computation	computation	NOUN
ejpam-412	373	27	,	,	PUNCT
ejpam-412	373	28	136	136	NUM
ejpam-412	373	29	,	,	PUNCT
ejpam-412	373	30	(	(	PUNCT
ejpam-412	373	31	2001	2001	NUM
ejpam-412	373	32	)	)	PUNCT
ejpam-412	373	33	,	,	PUNCT
ejpam-412	373	34	259	259	NUM
ejpam-412	373	35	-	-	SYM
ejpam-412	373	36	270	270	NUM
ejpam-412	373	37	.	.	PUNCT
ejpam-412	374	1	[	[	X
ejpam-412	374	2	22	22	NUM
ejpam-412	374	3	]	]	X
ejpam-412	374	4	y.l.yeh	y.l.yeh	PROPN
ejpam-412	374	5	,	,	PUNCT
ejpam-412	374	6	m.j	m.j	PROPN
ejpam-412	374	7	.	.	PROPN
ejpam-412	374	8	jang	jang	PROPN
ejpam-412	374	9	and	and	CCONJ
ejpam-412	374	10	c.	c.	PROPN
ejpam-412	374	11	wang	wang	PROPN
ejpam-412	374	12	,	,	PUNCT
ejpam-412	374	13	analyzing	analyze	VERB
ejpam-412	374	14	the	the	DET
ejpam-412	374	15	free	free	ADJ
ejpam-412	374	16	vibrations	vibration	NOUN
ejpam-412	374	17	of	of	ADP
ejpam-412	374	18	a	a	DET
ejpam-412	374	19	plate	plate	NOUN
ejpam-412	374	20	using	use	VERB
ejpam-412	374	21	finite	finite	ADJ
ejpam-412	374	22	difference	difference	NOUN
ejpam-412	374	23	and	and	CCONJ
ejpam-412	374	24	differential	differential	ADJ
ejpam-412	374	25	transformation	transformation	NOUN
ejpam-412	374	26	method	method	NOUN
ejpam-412	374	27	,	,	PUNCT
ejpam-412	374	28	appllied	appllie	VERB
ejpam-412	374	29	mathematics	mathematic	NOUN
ejpam-412	374	30	and	and	CCONJ
ejpam-412	374	31	computation	computation	NOUN
ejpam-412	374	32	,	,	PUNCT
ejpam-412	374	33	178	178	NUM
ejpam-412	374	34	,	,	PUNCT
ejpam-412	374	35	2	2	NUM
ejpam-412	374	36	,	,	PUNCT
ejpam-412	374	37	(	(	PUNCT
ejpam-412	374	38	2006	2006	NUM
ejpam-412	374	39	)	)	PUNCT
ejpam-412	374	40	,	,	PUNCT
ejpam-412	374	41	493	493	NUM
ejpam-412	374	42	-	-	SYM
ejpam-412	374	43	501	501	NUM
ejpam-412	374	44	.	.	PUNCT
ejpam-412	375	1	[	[	X
ejpam-412	375	2	23	23	NUM
ejpam-412	375	3	]	]	PUNCT
ejpam-412	375	4	j.	j.	PROPN
ejpam-412	375	5	k.	k.	PROPN
ejpam-412	375	6	zhou	zhou	PROPN
ejpam-412	375	7	,	,	PUNCT
ejpam-412	375	8	differential	differential	ADJ
ejpam-412	375	9	transformation	transformation	NOUN
ejpam-412	375	10	and	and	CCONJ
ejpam-412	375	11	its	its	PRON
ejpam-412	375	12	application	application	NOUN
ejpam-412	375	13	for	for	ADP
ejpam-412	375	14	electrical	electrical	ADJ
ejpam-412	375	15	circutits	circutit	NOUN
ejpam-412	375	16	,	,	PUNCT
ejpam-412	375	17	huarjung	huarjung	PROPN
ejpam-412	375	18	university	university	PROPN
ejpam-412	375	19	press	press	NOUN
ejpam-412	375	20	,	,	PUNCT
ejpam-412	375	21	wuhahn	wuhahn	PROPN
ejpam-412	375	22	,	,	PUNCT
ejpam-412	375	23	china	china	PROPN
ejpam-412	375	24	,	,	PUNCT
ejpam-412	375	25	1986	1986	NUM
ejpam-412	375	26	,	,	PUNCT
ejpam-412	375	27	(	(	PUNCT
ejpam-412	375	28	in	in	ADP
ejpam-412	375	29	chinese	chinese	PROPN
ejpam-412	375	30	)	)	PUNCT
ejpam-412	375	31	.	.	PUNCT